Question

Determine if triangle L, M, NLMN and triangle O, P, QOPQ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
L
M
N
O
P
Q
15
16
54°
77
80
54°
60°
Answer
Attempt 1 out of 2

The triangles
similar.

Answer 1

I can’t be sure from the text-only layout, but with the usual interpretation (triangle LMN has two sides 15 and 16 with included angle 54°, triangle OPQ has the corresponding two sides 77 and 80 with included angle 54°) the triangles are not similar.

Reason: for SAS similarity the ratios of the two pairs of corresponding sides must be equal and the included angles must be equal. Here the included angles are equal (54°), but
15/77 ≈ 0.1948 while 16/80 = 0.2000, so the side ratios are not equal. Also there is not a pair of two equal angles (only one 54° is given), so AA similarity fails. Thus the triangles are not similar.

If my reading of which numbers label which sides/angles is wrong, please repost the diagram or say which side/angle each number labels and I’ll re-check.