Question

Analyzing a Claim
Triangle M N O. Angle M is 72 degrees and angle O is 71.2 degrees. Triangle R S T. Angle R is 72 degrees and angle T is 36.8 degrees.

Isabelle claims that Triangle M N O is similar to triangle R S T. Is she correct? If not, what is her mistake?
Yes, she is correct.
No, the triangles are congruent because all corresponding sides and angles are congruent.
No, the vertices in her claim are not written in corresponding order.
No, her claim cannot be made about triangles with only one pair of congruent corresponding angles.

Answer 1

No — her triangles are similar, but she wrote the vertex correspondence incorrectly.

Compute the missing angles: in MNO, ∠N = 180 − 72 − 71.2 = 36.8°. So the angles of MNO are 72° (M), 36.8° (N), 71.2° (O). The angles of RST are 72° (R), 71.2° (S), 36.8° (T). Thus the correct correspondence is M ↔ R, N ↔ T, O ↔ S. Isabelle wrote M ↔ R, N ↔ S, O ↔ T, which is not correct.