Question

Are these triangles similar? if so, what postulate or theorem justifies that they are similar?

Answer 1

Yes The triangles are similar by SAS Similarity Theorem

Explanation:

we know that

Side-Angle-Side Similarity, states that If an angle of a triangle is congruent to an angle of another triangle and if the included sides of these angles are proportional, then the two triangles are similar

In this problem

Angle L is congruent with Angle Z

so

Verify if the included sides are proportional

so

`(LJ)/(ZY)=(KL)/(XZ)`

substitute the values

`(3)/(1.5)=(4)/(2)`

`2=2` -----> is true

therefore

The triangles are similar by SAS