Chapter 46: Properties of Two-Dimensional Shapes

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review

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Chapter Overview

This chapter teaches Properties of Two-Dimensional Shapes in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

Two-dimensional shape properties (Two-dimensional shape properties is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Triangles (Triangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Quadrilaterals (Quadrilaterals is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Squares (Squares is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Rectangles (Rectangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Parallelograms (Parallelograms is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

46.1 Two-dimensional shape properties

Two-dimensional shape properties is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Two-dimensional shape properties. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.2 Triangles

Triangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Triangles. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.3 Quadrilaterals

Quadrilaterals is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Quadrilaterals. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.4 Squares

Squares is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Squares. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.5 Rectangles

Rectangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Rectangles. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.6 Parallelograms

Parallelograms is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Parallelograms. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.7 Rhombuses

Rhombuses is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Rhombuses. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.8 Trapezoids

Trapezoids is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Trapezoids. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.9 Kites

Kites is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Kites. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.10 Parallel sides

Parallel sides is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Parallel sides. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.11 Perpendicular sides

Perpendicular sides is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Perpendicular sides. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.12 Angle properties

Angle properties is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Classify an angle measuring 35°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 2

Problem: Classify an angle measuring 48°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 3

Problem: Classify an angle measuring 67°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 4

Problem: Classify an angle measuring 72°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 5

Problem: Classify an angle measuring 110°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Obtuse

Worked Example 6

Problem: Classify an angle measuring 25°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 7

Problem: Classify an angle measuring 58°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 8

Problem: Classify an angle measuring 83°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Acute

Worked Example 9

Problem: Classify an angle measuring 95°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Obtuse

Worked Example 10

Problem: Classify an angle measuring 120°.

Compare the measure with 90° and 180°.

Very beginner explanation: Angle names depend on their measure.

Answer: Obtuse

Practice Exercise

Create one new Grade 6 problem about Angle properties. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

46.13 Line symmetry

Line symmetry is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Line symmetry. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

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30 Review Questions and Answers

Q1. What is important to understand about Two-dimensional shape properties?

Answer: Two-dimensional shape properties is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Triangles?

Answer: Triangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Quadrilaterals?

Answer: Quadrilaterals is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Squares?

Answer: Squares is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Rectangles?

Answer: Rectangles is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Parallelograms?

Answer: Parallelograms is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Rhombuses?

Answer: Rhombuses is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q8. What is important to understand about Trapezoids?

Answer: Trapezoids is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Kites?

Answer: Kites is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Parallel sides?

Answer: Parallel sides is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Perpendicular sides?

Answer: Perpendicular sides is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Angle properties?

Answer: Angle properties is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Line symmetry?

Answer: Line symmetry is a Grade 6 mathematics idea in Properties of Two-Dimensional Shapes. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q16. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q23. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q24. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q25. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q26. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q27. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q28. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q29. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q30. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.