Mathematics Class 7 - Congruence Of-Triangles Notes

Congruence of Triangles

Welcome to the chapter on Congruence of Triangles for Class 7. In this chapter, you will learn what congruence means, how to check if two triangles are congruent, and the rules for triangle congruence. By the end of this chapter, you will be able to identify and prove congruent triangles using different criteria!

Introduction

Congruence means "exactly equal in shape and size." Two figures are congruent if they have the same size and shape. In geometry, we often check if two triangles are congruent.

What is Congruence?

• Congruent figures have the same size and shape.
• If you place one on top of the other, they match exactly.
• Symbol for congruence: ≅

Congruence of Triangles

Two triangles are congruent if their sides and angles are equal. There are special rules to check triangle congruence.

Rules for Congruence of Triangles

• SSS (Side-Side-Side): If all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent.
• SAS (Side-Angle-Side): If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, the triangles are congruent.
• ASA (Angle-Side-Angle): If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, the triangles are congruent.
• AAS (Angle-Angle-Side): If two angles and any side in one triangle are equal to two angles and any side in another triangle, the triangles are congruent.
• RHS (Right angle-Hypotenuse-Side): For right-angled triangles, if the hypotenuse and one side are equal, the triangles are congruent.

How to Prove Triangles are Congruent?

• Compare the sides and angles of both triangles.
• Use one of the congruence rules (SSS, SAS, ASA, AAS, RHS).
• Write a statement: △ABC ≅ △DEF

Fun Activity: Cut and Match!

Cut out two triangles of the same size from paper. Place one on top of the other to see if they match. Try with different sizes and shapes!

Summary

• Congruent triangles have equal sides and angles.
• Use SSS, SAS, ASA, AAS, or RHS rules to check congruence.
• Congruence helps us solve geometric problems and proofs.

Practice Questions

1. State the SSS rule for triangle congruence.
2. If two triangles have two sides and the angle between them equal, which rule applies?
3. What is the symbol for congruence?
4. Name the rule used for right-angled triangles.
5. Are two triangles with equal angles but different side lengths congruent?

Challenge Yourself

• Draw two congruent triangles and label their sides and angles.
• Find two objects at home that are congruent in shape and size.

Did You Know?

• Congruence is used in making patterns and designs!
• Architects use congruent shapes to build strong structures.

Glossary

• Congruent: Exactly equal in shape and size.
• Triangle: A shape with three sides and three angles.
• Hypotenuse: The longest side in a right-angled triangle.
• Proof: Showing something is true using rules and logic.

Answers to Practice Questions

1. If all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent.
2. SAS (Side-Angle-Side) rule.
3. ≅
4. RHS (Right angle-Hypotenuse-Side) rule.
5. No, their sides must also be equal.

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Practice congruence rules to master triangle problems in geometry!