Question

Are the two triangles below similar?
A: Yes; they have congruent corresponding angles
B: No; they do not have congruent corresponding angles
C: Yes; they have proportional corresponding sides
D: No; they do not have proportional corresponding sides

Answer 1

Triangle DEF:

m<D + m<E + m<F = 180

m<D + 58 + 38 = 180

m<D + 96 = 180

m<D = 84

Now you have triangle DEF with two angles measuring 84 and 38 degrees. There are two angles in triangle ABC that also measure 84 and 58 degrees, so by AA, the triangles are similar.

Answer: A: Yes; they have congruent corresponding angles