Which triangle is △ABC similar to and why?

Question

asked Oct 2, 2019 176k views

2 Answers

Polemarch · Answer 1 · 2019-10-07T13:59:29+0000

Answer:

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.