Chapter 50: Congruent Triangles, Rectangles, and Parallelograms
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Congruent Triangles, Rectangles, and Parallelograms with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Meaning of congruent (a Grade 5 idea used in this chapter)
- Matching corresponding sides (a Grade 5 idea used in this chapter)
- Matching corresponding angles (a Grade 5 idea used in this chapter)
- Congruent triangles (a Grade 5 idea used in this chapter)
- Congruent rectangles (a Grade 5 idea used in this chapter)
- Congruent parallelograms (a Grade 5 idea used in this chapter)
- Tracing to test congruence (a Grade 5 idea used in this chapter)
- Rotating a shape without changing congruence (a Grade 5 idea used in this chapter)
- Reflecting a shape without changing congruence (a Grade 5 idea used in this chapter)
- Constructing congruent figures (a Grade 5 idea used in this chapter)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
50.1 Meaning of congruent
Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Meaning of congruent?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Worked Example 2
Problem: What should you identify first before solving a problem about Meaning of congruent?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Meaning of congruent.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Meaning of congruent problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Meaning of congruent.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of congruent can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Meaning of congruent. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.2 Matching corresponding sides
Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Matching corresponding sides?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Matching corresponding sides?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Matching corresponding sides.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Matching corresponding sides problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Matching corresponding sides.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Matching corresponding sides can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Matching corresponding sides in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Matching corresponding sides becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Matching corresponding sides and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Matching corresponding sides becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Matching corresponding sides using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Matching corresponding sides becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Matching corresponding sides problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Matching corresponding sides becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Matching corresponding sides could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Matching corresponding sides becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Matching corresponding sides. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.3 Matching corresponding angles
Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Matching corresponding angles?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Matching corresponding angles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Matching corresponding angles.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Matching corresponding angles problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Matching corresponding angles.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Matching corresponding angles can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Matching corresponding angles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.4 Congruent triangles
Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Congruent triangles?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Congruent triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Congruent triangles.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Congruent triangles problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Congruent triangles.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent triangles can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: A triangle has angles 35° and 50°. Find the third angle.
- Triangle angles total 180°.
- 180 - 35 - 50 = 95.
Very beginner explanation: Subtract the known angles from 180°.
Answer: 95°
Worked Example 7
Problem: A triangle has angles 48° and 50°. Find the third angle.
- Triangle angles total 180°.
- 180 - 48 - 50 = 82.
Very beginner explanation: Subtract the known angles from 180°.
Answer: 82°
Worked Example 8
Problem: A triangle has angles 67° and 50°. Find the third angle.
- Triangle angles total 180°.
- 180 - 67 - 50 = 63.
Very beginner explanation: Subtract the known angles from 180°.
Answer: 63°
Worked Example 9
Problem: A triangle has angles 72° and 50°. Find the third angle.
- Triangle angles total 180°.
- 180 - 72 - 50 = 58.
Very beginner explanation: Subtract the known angles from 180°.
Answer: 58°
Worked Example 10
Problem: A triangle has angles 110° and 50°. Find the third angle.
- Triangle angles total 180°.
- 180 - 110 - 50 = 20.
Very beginner explanation: Subtract the known angles from 180°.
Answer: 20°
Practice Exercise
Create one new question about Congruent triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.5 Congruent rectangles
Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Congruent rectangles?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Congruent rectangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Congruent rectangles.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Congruent rectangles problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Congruent rectangles.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent rectangles can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Congruent rectangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.6 Congruent parallelograms
Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Congruent parallelograms?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Congruent parallelograms?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Congruent parallelograms.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Congruent parallelograms problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Congruent parallelograms.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Congruent parallelograms can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Congruent parallelograms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.7 Tracing to test congruence
Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Tracing to test congruence?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Tracing to test congruence?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Tracing to test congruence.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Tracing to test congruence problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Tracing to test congruence.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Tracing to test congruence can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Tracing to test congruence in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tracing to test congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Tracing to test congruence and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tracing to test congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Tracing to test congruence using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tracing to test congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Tracing to test congruence problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tracing to test congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Tracing to test congruence could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tracing to test congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Tracing to test congruence. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.8 Rotating a shape without changing congruence
Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Rotating a shape without changing congruence?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Rotating a shape without changing congruence?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Rotating a shape without changing congruence.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Rotating a shape without changing congruence problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Rotating a shape without changing congruence.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Rotating a shape without changing congruence can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Rotating a shape without changing congruence in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Rotating a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Rotating a shape without changing congruence and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Rotating a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Rotating a shape without changing congruence using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Rotating a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Rotating a shape without changing congruence problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Rotating a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Rotating a shape without changing congruence could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Rotating a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Rotating a shape without changing congruence. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.9 Reflecting a shape without changing congruence
Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Reflecting a shape without changing congruence?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Reflecting a shape without changing congruence?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Reflecting a shape without changing congruence.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Reflecting a shape without changing congruence problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Reflecting a shape without changing congruence.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Reflecting a shape without changing congruence can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Reflecting a shape without changing congruence in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Reflecting a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Reflecting a shape without changing congruence and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Reflecting a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Reflecting a shape without changing congruence using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Reflecting a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Reflecting a shape without changing congruence problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Reflecting a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Reflecting a shape without changing congruence could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Reflecting a shape without changing congruence becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Reflecting a shape without changing congruence. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
50.10 Constructing congruent figures
Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Constructing congruent figures?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Constructing congruent figures?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Constructing congruent figures.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Constructing congruent figures problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Constructing congruent figures.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing congruent figures can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Constructing congruent figures. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Meaning of congruent.
- Create and solve one original problem about Matching corresponding sides.
- Create and solve one original problem about Matching corresponding angles.
- Create and solve one original problem about Congruent triangles.
- Create and solve one original problem about Congruent rectangles.
- Create and solve one original problem about Congruent parallelograms.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Meaning of congruent?
Answer: Meaning of congruent helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q2. What is the key idea in Matching corresponding sides?
Answer: Matching corresponding sides is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q3. What is the key idea in Matching corresponding angles?
Answer: Matching corresponding angles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q4. What is the key idea in Congruent triangles?
Answer: Congruent triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q5. What is the key idea in Congruent rectangles?
Answer: Congruent rectangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q6. What is the key idea in Congruent parallelograms?
Answer: Congruent parallelograms develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q7. What is the key idea in Tracing to test congruence?
Answer: Tracing to test congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q8. What is the key idea in Rotating a shape without changing congruence?
Answer: Rotating a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q9. What is the key idea in Reflecting a shape without changing congruence?
Answer: Reflecting a shape without changing congruence is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q10. What is the key idea in Constructing congruent figures?
Answer: Constructing congruent figures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 5 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Congruent Triangles, Rectangles, and Parallelograms effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Congruent Triangles, Rectangles, and Parallelograms effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Congruent Triangles, Rectangles, and Parallelograms effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Congruent Triangles, Rectangles, and Parallelograms effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Congruent Triangles, Rectangles, and Parallelograms effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.