SAS test

The SAS similarity test: If the ratio of the lengths of two sides of one triangle is equal to the ratio of the lengths of two sides of another triangle, and the included angles are equal, then the two triangles are similar.

Detailed description

Example 3

Prove that \(\triangle ABC\) is similar to \(\triangle DEC\).

Detailed description

Solution

In the triangles \(ABC\) and \(DEC\)

\begin{align}\dfrac{AC}{BC}&=\dfrac{3}{7}(given)\\ \dfrac{DC}{EC}&=\dfrac{3}{7}(given)\\ \angle ACE&= \angle DCE\ (\text{vertically opposite})\end{align}

So \(\triangle ABC\) is similar to \(\triangle DEC\) (SAS similarity test).