Question

identify the similar triangles.
a) △bca ~△bde
b) △abc ~△dbe
c) △cba ~△bde
d) △bac ~△bed

Explanation:

Step1: Check angle - angle similarity

We know that $\angle ABC=\angle DBE = 90^{\circ}$. Also, $\angle BCA$ and $\angle BED$ are vertical - angles, so $\angle BCA=\angle BED$. By the AA (angle - angle) similarity criterion, the two triangles are similar.

Step2: Match the corresponding vertices

The vertices of the similar triangles should be matched correctly. In $\triangle ABC$ and $\triangle DBE$, $\angle A$ corresponds to $\angle D$, $\angle B$ corresponds to $\angle B$ (the right - angle vertex), and $\angle C$ corresponds to $\angle E$. So, $\triangle ABC\sim\triangle DBE$.

Answer:

B. $\triangle ABC\sim\triangle DBE$