Question

Why are these triangles similar?

A. Angle-Angle similarity
B. Side-Angle-Side similarity
C. Side-Side-Side similarity
D. The triangle are not similar

Answer 1

B. Side-Angle-Side similarity

Explanation:

Since Angle A and Angle X are marked congruent (same) and the sides just to the left and just to the right of both of these angle have the same ratio:

8/4 = 10/5

(as well as

4/8 = 5/10)

Then the two triangles are similar by Side-Angle-Side, SAS.

Answer A and C are real reasons for similarity, but we are not given two angles, nor all three (six!) sides...so not enough info to use AA or SSS. So the answer is NOT A and NOT C. The triangles are similar by SAS (Answer B) so D is wrong as well.