Chapter 46: Quadrilaterals and Polygons
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Quadrilaterals and Polygons with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
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.
46.1 Quadrilateral
A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral .
Answer: Use the listed property to classify the shape.
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 Quadrilateral. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.2 Square
Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 6
Problem: Explain Square 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: Square 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 Square 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: Square 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 Square 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: Square 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 Square 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: Square 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 Square 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: Square 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 Square. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.3 Rectangle
An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find supplementary angle to 35°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Answer: 145°
Worked Example 2
Problem: Find supplementary angle to 48°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Answer: 132°
Worked Example 3
Problem: Find supplementary angle to 67°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Answer: 113°
Worked Example 4
Problem: Find supplementary angle to 72°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Answer: 108°
Worked Example 5
Problem: Find supplementary angle to 110°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle .
Answer: 70°
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 Rectangle. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.4 Parallelogram
Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find supplementary angle to 35°.
- Supplementary angles total 180°.
Very beginner explanation: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Answer: 145°
Worked Example 2
Problem: Find supplementary angle to 48°.
- Supplementary angles total 180°.
Very beginner explanation: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Answer: 132°
Worked Example 3
Problem: Find supplementary angle to 67°.
- Supplementary angles total 180°.
Very beginner explanation: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Answer: 113°
Worked Example 4
Problem: Find supplementary angle to 72°.
- Supplementary angles total 180°.
Very beginner explanation: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Answer: 108°
Worked Example 5
Problem: Find supplementary angle to 110°.
- Supplementary angles total 180°.
Very beginner explanation: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram .
Answer: 70°
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 Parallelogram. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.5 Rhombus
Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 6
Problem: Explain Rhombus 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: Rhombus 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 Rhombus 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: Rhombus 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 Rhombus 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: Rhombus 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 Rhombus 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: Rhombus 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 Rhombus 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: Rhombus 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 Rhombus. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.6 Trapezoid
Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 6
Problem: Explain Trapezoid 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: Trapezoid 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 Trapezoid 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: Trapezoid 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 Trapezoid 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: Trapezoid 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 Trapezoid 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: Trapezoid 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 Trapezoid 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: Trapezoid 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 Trapezoid. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.7 Kite
Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use the listed property to classify the shape.
Worked Example 6
Problem: Explain Kite 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: Kite 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 Kite 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: Kite 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 Kite 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: Kite 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 Kite 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: Kite 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 Kite 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: Kite 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 Kite. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.8 Properties of quadrilaterals
A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals .
Answer: Use the listed property to classify the shape.
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 Properties of quadrilaterals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.9 Polygons
A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons .
Answer: Use the listed property to classify the shape.
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 Polygons. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.10 Regular polygons
A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons .
Answer: Use the listed property to classify the shape.
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 Regular polygons. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.11 Irregular polygons
A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons .
Answer: Use the listed property to classify the shape.
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 Irregular polygons. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.12 Naming polygons
A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons .
Answer: Use the listed property to classify the shape.
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 Naming polygons. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.13 Interior-angle ideas
An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find supplementary angle to 35°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Answer: 145°
Worked Example 2
Problem: Find supplementary angle to 48°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Answer: 132°
Worked Example 3
Problem: Find supplementary angle to 67°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Answer: 113°
Worked Example 4
Problem: Find supplementary angle to 72°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Answer: 108°
Worked Example 5
Problem: Find supplementary angle to 110°.
- Supplementary angles total 180°.
Very beginner explanation: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas .
Answer: 70°
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 Interior-angle ideas. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
46.14 Symmetry in polygons
A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: State one defining/property clue for a Square.
- 4 equal sides; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Answer: Use the listed property to classify the shape.
Worked Example 2
Problem: State one defining/property clue for a Rectangle.
- opposite sides equal; 4 right angles
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Answer: Use the listed property to classify the shape.
Worked Example 3
Problem: State one defining/property clue for a Parallelogram.
- opposite sides parallel and equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Answer: Use the listed property to classify the shape.
Worked Example 4
Problem: State one defining/property clue for a Rhombus.
- 4 equal sides; opposite angles equal
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Answer: Use the listed property to classify the shape.
Worked Example 5
Problem: State one defining/property clue for a Trapezoid.
- at least one pair of parallel sides
Very beginner explanation: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons .
Answer: Use the listed property to classify the shape.
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 Symmetry in polygons. 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 complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Quadrilateral . Show your reasoning and check your answer.
- Create and solve a new question about Square . Show your reasoning and check your answer.
- Create and solve a new question about Rectangle . Show your reasoning and check your answer.
- Create and solve a new question about Parallelogram . Show your reasoning and check your answer.
- Create and solve a new question about Rhombus . Show your reasoning and check your answer.
- Create and solve a new question about Trapezoid . Show your reasoning and check your answer.
- Create and solve a new question about Kite . Show your reasoning and check your answer.
- Create and solve a new question about Properties of quadrilaterals . Show your reasoning and check your answer.
- Create and solve a new question about Polygons . Show your reasoning and check your answer.
- Create and solve a new question about Regular polygons . Show your reasoning and check your answer.
- Create and solve a new question about Irregular polygons . Show your reasoning and check your answer.
- Create and solve a new question about Naming polygons . Show your reasoning and check your answer.
Common Mistakes
- Assuming a diagram is drawn to scale.
- Confusing radius and diameter.
- Using square units for volume or cubic units for area.
- Applying a scale factor to only one dimension.
- Forgetting the circular bases in cylinder surface area.
30 Review Questions and Answers
Q1. What is important to remember about Quadrilateral?
Answer: A quadrilateral is a four-sided polygon. This topic focuses on Quadrilateral.
Q2. What is important to remember about Square?
Answer: Square is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Rectangle?
Answer: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Rectangle.
Q4. What is important to remember about Parallelogram?
Answer: Parallel lines lie in the same plane and never meet. This topic focuses on Parallelogram.
Q5. What is important to remember about Rhombus?
Answer: Rhombus is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Trapezoid?
Answer: Trapezoid is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Kite?
Answer: Kite is an important Grade 7 idea in Quadrilaterals and Polygons. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Properties of quadrilaterals?
Answer: A quadrilateral is a four-sided polygon. This topic focuses on Properties of quadrilaterals.
Q9. What is important to remember about Polygons?
Answer: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Polygons.
Q10. What is important to remember about Regular polygons?
Answer: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Regular polygons.
Q11. What is important to remember about Irregular polygons?
Answer: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Irregular polygons.
Q12. What is important to remember about Naming polygons?
Answer: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Naming polygons.
Q13. What is important to remember about Interior-angle ideas?
Answer: An angle is formed by two rays meeting at a vertex and is measured in degrees. This topic focuses on Interior-angle ideas.
Q14. What is important to remember about Symmetry in polygons?
Answer: A polygon is a closed 2D figure made from straight line segments. This topic focuses on Symmetry in polygons.
Q15. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q16. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q17. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q18. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q19. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q20. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q21. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q22. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q23. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q24. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q25. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q26. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q27. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q28. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q29. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q30. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.