Congruent shapes

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

Various 6 sided shapes, labelled A - H. 3 shapes 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)

Pair of SSS triangles

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

Pair of ASA triangles

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

Pair of SAS triangles

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

Pair of RHS triangles

Example 1

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

Pair of SSS triangles (lengths: 5.5cm, 4cm & 3cm)

Yes - SSS, the three sides are equal.

Example 2

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

Pair of RHS triangles (lengths: 5.8cm, 3cm & right angle) (lengths: 58mm, 30mm & right angle)

Yes - RHS.

Question

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

Triangle 1 - angles of 60 and 40 degrees. Side of 7cm between angles Triangle 2 - angles of 60 and 40 degrees. Side of 7cm next to 60 degree angle

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.