Concepts of Congruence and Similarity

Concepts of Congruence and Similarity

GCSE(F), GCSE(H),

Congruent shapes have the same angles and lengths as each other, although they may be subject to reflection and/or rotation.

Similar shapes have the same angles as each other, but will have different lengths. One shape will be an enlargement of another. Each side length will be the same multiple larger than the corresponding side on the other shape.

The lengths on the similar triangle are all 1.5x larger than on the original triangle.

Examples

1. Two triangles are shown below. The corresponding angles on both triangles are the same. What is the length of the side XZ?

Answer: 6 cm

BC is twice the size of the corresponding side YZ.

The enlargement is a scale factor of 0.5.

AC x 0.5 = 12 x 0.5 = 6 cm

2. What is the length of the larger rectangle?

Answer: 250 mm

The larger rectangle is an enlargement of `frac(125)(100)` = 1.25

1.25 x 200 = 250 mm