Chapter 49: Triangle Properties and Construction
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Triangle Properties and Construction with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Sides, vertices, and angles of triangles (a Grade 5 idea used in this chapter)
- Acute triangles (a Grade 5 idea used in this chapter)
- Right triangles (a Grade 5 idea used in this chapter)
- Obtuse triangles (a Grade 5 idea used in this chapter)
- Equilateral triangles (a Grade 5 idea used in this chapter)
- Isosceles triangles (a Grade 5 idea used in this chapter)
- Scalene triangles (a Grade 5 idea used in this chapter)
- Classifying triangles in two ways (a Grade 5 idea used in this chapter)
- Constructing triangles from side measures (a Grade 5 idea used in this chapter)
- Constructing triangles from angle information (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.
49.1 Sides, vertices, and angles of triangles
Sides, vertices, and angles of 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 Sides, vertices, and angles of 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: Sides, vertices, and angles of triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Sides, vertices, and angles of 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 Sides, vertices, and angles of triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Sides, vertices, and angles of 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 Sides, vertices, and angles of 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: Sides, vertices, and angles of 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 Sides, vertices, and angles of 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: Sides, vertices, and angles of 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 Sides, vertices, and angles of 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: Sides, vertices, and angles of triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Sides, vertices, and angles of 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 Sides, vertices, and angles of triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.2 Acute triangles
Acute 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 Acute 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: Acute triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Acute 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 Acute triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Acute 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 Acute 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: Acute 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 Acute 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: Acute 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 Acute 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: Acute triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Acute 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 Acute triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.3 Right triangles
Right 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 Right 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: Right triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Right 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 Right triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Right 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 Right 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: Right 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 Right 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: Right 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 Right 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: Right triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Right 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 Right triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.4 Obtuse triangles
Obtuse 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 Obtuse 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: Obtuse triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Obtuse 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 Obtuse triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Obtuse 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 Obtuse 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: Obtuse 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 Obtuse 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: Obtuse 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 Obtuse 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: Obtuse triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Obtuse 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 Obtuse triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.5 Equilateral triangles
Equilateral 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 Equilateral 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: Equilateral triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Equilateral 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 Equilateral triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Equilateral 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 Equilateral 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: Equilateral 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 Equilateral 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: Equilateral 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 Equilateral 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: Equilateral triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Equilateral 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 Equilateral triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.6 Isosceles triangles
Isosceles 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 Isosceles 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: Isosceles triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Isosceles 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 Isosceles triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Isosceles 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 Isosceles 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: Isosceles 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 Isosceles 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: Isosceles 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 Isosceles 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: Isosceles triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Isosceles 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 Isosceles triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.7 Scalene triangles
Scalene 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 Scalene 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: Scalene triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Scalene 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 Scalene triangles?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Scalene 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 Scalene 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: Scalene 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 Scalene 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: Scalene 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 Scalene 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: Scalene triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Scalene 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 Scalene triangles. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.8 Classifying triangles in two ways
Classifying triangles in two ways 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 Classifying triangles in two ways?
- 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: Classifying triangles in two ways develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Classifying triangles in two ways 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 Classifying triangles in two ways?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Classifying triangles in two ways 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 Classifying triangles in two ways.
- 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: Classifying triangles in two ways 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 Classifying triangles in two ways 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: Classifying triangles in two ways 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 Classifying triangles in two ways.
- 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: Classifying triangles in two ways develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Classifying triangles in two ways 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 Classifying triangles in two ways. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.9 Constructing triangles from side measures
Constructing triangles from side measures 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 triangles from side measures?
- 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 triangles from side measures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing triangles from side measures 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 triangles from side measures?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Constructing triangles from side measures 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 triangles from side measures.
- 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 triangles from side measures 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 triangles from side measures 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 triangles from side measures 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 triangles from side measures.
- 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 triangles from side measures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing triangles from side measures 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 Constructing triangles from side measures. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
49.10 Constructing triangles from angle information
Constructing triangles from angle information 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 triangles from angle information?
- 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 triangles from angle information develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing triangles from angle information 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 triangles from angle information?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Constructing triangles from angle information 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 triangles from angle information.
- 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 triangles from angle information 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 triangles from angle information 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 triangles from angle information 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 triangles from angle information.
- 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 triangles from angle information develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Constructing triangles from angle information 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 Constructing triangles from angle information. 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 Sides, vertices, and angles of triangles.
- Create and solve one original problem about Acute triangles.
- Create and solve one original problem about Right triangles.
- Create and solve one original problem about Obtuse triangles.
- Create and solve one original problem about Equilateral triangles.
- Create and solve one original problem about Isosceles triangles.
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 Sides, vertices, and angles of triangles?
Answer: Sides, vertices, and angles of triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q2. What is the key idea in Acute triangles?
Answer: Acute triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q3. What is the key idea in Right triangles?
Answer: Right triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q4. What is the key idea in Obtuse triangles?
Answer: Obtuse triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q5. What is the key idea in Equilateral triangles?
Answer: Equilateral triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q6. What is the key idea in Isosceles triangles?
Answer: Isosceles triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q7. What is the key idea in Scalene triangles?
Answer: Scalene triangles develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q8. What is the key idea in Classifying triangles in two ways?
Answer: Classifying triangles in two ways develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q9. What is the key idea in Constructing triangles from side measures?
Answer: Constructing triangles from side measures develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q10. What is the key idea in Constructing triangles from angle information?
Answer: Constructing triangles from angle information 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 Triangle Properties and Construction 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 Triangle Properties and Construction 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 Triangle Properties and Construction 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 Triangle Properties and Construction 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 Triangle Properties and Construction effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.