Section 3.4: Using Similar Triangles

Property

Two figures are similar if the measures of their corresponding angles are equal and their corresponding sides are in the same ratio. For triangles, if $\triangle ABC$ is similar to $\triangle XYZ$, this property holds true.

Corresponding angles are equal:
$\operatorname{m}\angle A = \operatorname{m}\angle X$
$\operatorname{m}\angle B = \operatorname{m}\angle Y$
$\operatorname{m}\angle C = \operatorname{m}\angle Z$

Corresponding sides are in the same ratio:

Property

For any $\triangle ABC$, the sum of the measures of the angles is $180^\circ$.

Examples

• The measures of two angles of a triangle are $60^\circ$ and $85^\circ$. The third angle, $x$, is found by solving $60^\circ + 85^\circ + x = 180^\circ$, which gives $145^\circ + x = 180^\circ$, so $x = 35^\circ$.