# Apply Congruency Rules

In this worksheet, students will apply the congruency rules to problems.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Identify and Construct Congruent Triangles

Difficulty level:

#### Worksheet Overview

Shapes that are exactly the same shape and size are congruent.

Triangles

We have a set of rules which make a triangle congruent!

If these rules apply then the triangles are congruent!

1) Three matching sides (SSS)

2) Two matching sides and the angle between them (SAS)

3) Two matching angles and a corresponding side (AAS)

4) In a right-angled triangle, the hypotenuse and one matching side (RHS)

Make a note of the four rules and we will look at an example question.

Example

The triangles below are congruent.

State the condition that shows they are congruent.

Well, the choices we have are:

SSS - all 3 sides are the same

SAS - 2 matching sides and the angle between

AAS - 2 matching angles and a corresponding side

RHS - Right angle, hypotenuse and a matching side

All the sides are the same - 4 and 4, 5 and 5 and 7 and 7

So, we can say they are congruent, as the condition is SSS

There's a lot to remember here, but you can look back at this introduction at any point by clicking on the red help button on the screen.

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