Ratios and Similarity

# Ratios and Similarity

GCSE(F), GCSE(H),

Ratios are used to determine similarity between geometric shapes.

Two triangles are shown in the diagram: ABC and ADE. The lines BC and DE are parallel. All the angles in the triangle are equal, and therefore the triangles are similar.

The ratios of the lengths of the sides BC : DE are 12 : 32, which can be simplified to 3 : 8.

The other lengths are all in same ratio If AB is 24cm, then AD is frac(24 xx 8)(3) = 64cm.

## Examples

1. If, on the above diagram, AC is 22cm, then what is the length AE?

The ratio for the lengths is 3 : 8. AC is 22cm, the length AE is frac(22 xx 8)(3) = 58.67cm