If the angles of one triangle are
equal to the angles of another triangle, then the triangles are said to be equiangular.

Equiangular triangles have the same shape but may have different
sizes. So, equiangular triangles are also called similar
triangles.

For example, triangle DEF is similar to triangle ABC as
their three angles are equal.

The length of each side in triangle DEF is multiplied by the
same number, 3, to give the sides of triangle ABC.

In general:

If two triangles are similar, then the corresponding sides are
in the same ratio.

Example 26

Find the value of x in the following pair of
triangles.

Solution:

Note:

Equal angles are marked in the same way in diagrams.

Example 27

Find the value of the pronumeral in the following diagram.

Solution:

Applications of Similarity

Similar triangles can be applied to solve real world problems.

Example 28

Find the value of the height, h m, in the following diagram at
which the tennis ball must be hit so that it will just pass over the net
and land 6 metres away from the base of the net.

Solution:

So, the height at which the ball should be hit is 2.7 m.

Note:

a. Equal angles are marked in the same way in diagrams.

b. Two triangles are similar if:

two pairs of corresponding sides are in the same ratio and the
angle included between them are equal.