Question

are the triangles similar ? If yes state how

Answer 1

Given:

The objective is to find whether the two triangles are similar or not with explanation.

The given triangles can be represented as,

From the given figure, the sides AB = AC = 13.5 and the sides DE = DF = 7.5.

For two triangles to be similar, the ratio of their adjacent sides should be equal.

The ratios are,

$\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}$

Now, apply the given values in the above ratio.

$\begin{gathered} \frac{13.5}{7.5}=\frac{13.5}{7.5}=\frac{9}{5} \\ 1.8=1.8=1.8 \end{gathered}$

Thus, the ratios of sides of the two triangles are similar.

Hence, the two triangles are similar triangles.