Question

Determine whether the triangles are similar. or not.

Answer 1

Answer:

A

Step-by-step explanation:

We know that ∠$ABE$ ≅ ∠$DBC$ because they are vertical angles, so that's one pair of congruent angles. However, we can't compare ∠$BAE$ and ∠$DCB$ as they have different measures, so we'll have to find the measure of either ∠$AEB$ or ∠$BDC$. Let's go with the former. Using the fact that the sum of the measures of the interior angles of a triangle is $180$°, we know that $m$∠$AEB=180-(53+42)=180-95=85$°. Now, we know that ∠$AEB$ ≅ ∠$DCB$ because their measures are equal. That's another pair of congruent angles. Therefore, the angles are similar by $AA$. Hope this helps!