# Congruence and similarity

### 1) Congruent shapes

Two shapes that are the same size and the same shape are congruent.

Shapes A, B, E and G are congruent. They are identical in size and shape.

##### Congruent triangles

For two triangles to be congruent, one of 4 criteria need to be met.

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

##### Example 1

State whether the two triangles are congruent. Give a reason to support your answer.

Yes – SSS, the three sides are equal.

##### Example 2

State whether the two triangles are congruent. Give a reason to support your answer.

Yes – RHS.

##### Example 3

State whether the two triangles are congruent. Give a reason to support your answer.

No – in the left hand diagram the 7 cm length is between the angles 40° and 60°. In the right hand diagram it is not.

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