EDEXCEL GCSE FOUNDATION MATHS - What are Congruent Triangles

Edexcel GCSE Foundation Maths: Congruent Triangles

What are Congruent Triangles?

Congruent triangles are triangles that are exactly the same size and shape. This means that all corresponding sides and angles are equal.

How to Identify Congruent Triangles

There are four ways to prove that two triangles are congruent:

1. SSS (Side-Side-Side): If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

2. SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

3. ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

4. RHS (Right Angle-Hypotenuse-Side): If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.

Examples

Example 1:

Triangles ABC and DEF are congruent because all three sides are equal: * AB = DE * BC = EF * AC = DF

This satisfies the SSS condition.

Example 2:

Triangles ABC and DEF are congruent because: * AB = DE * BC = EF * ?ABC = ?DEF

This satisfies the SAS condition.

Practice Problems

1. Identify which pairs of triangles are congruent and state the reason.

1. Two triangles have sides of length 5 cm, 7 cm, and 9 cm. Another triangle has sides of length 9 cm, 7 cm, and 5 cm. Are the triangles congruent? Why or why not?

2. Two triangles have two sides and an included angle equal. Are the triangles congruent? If yes, which condition applies?

Remember:

• Congruent triangles have the same size and shape.
• There are four ways to prove congruency: SSS, SAS, ASA, and RHS.
• Understanding congruent triangles is important for solving geometric problems.