Question

Which triangle is ​△ABC​ similar to and why?

Answer 1

ABC is similar to DEF

Answer 2

C. Triangle ABC is similar to triangle JEL by AA similarity postulate.

Explanation:

We have been given 4 triangles. We are asked to find which triangle is similar to triangle ABC.

We know that angles of triangle add up-to 180 degrees.

Let us find measure of angle C as:

`m\angle A+m\angle B+m\angle C=180^(\circ)`

`50^(\circ)+65^(\circ)+m\angle C=180^(\circ)`

`115^(\circ)+m\angle C=180^(\circ)`

`115^(\circ)-115^(\circ)+m\angle C=180^(\circ)-115^(\circ)`

`m\angle C=65^(\circ)`

We can see that in triangles ABC and JEL:

`m\angle B=m\angle E=65^(\circ)`

`m\angle C=m\angle L=65^(\circ)`

Therefore, triangle ABC is similar to triangle JEL by angle AA similarity postulate and option C is the correct choice.