Question

Determine if triangle J, K, LJKL and triangle M, N, OMNO are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
J
K
L
M
N
O
20
18
25
60
54
75
46

Answer 1

Yes — triangles JKL and MNO are similar.

Reason: the three side lengths of MNO are exactly 3 times the corresponding sides of JKL:
- 60 = 3·20, 54 = 3·18, 75 = 3·25,
so 60/20 = 54/18 = 75/25 = 3. By SSS similarity the triangles are similar (scale factor 3). A consistent correspondence is J ↔ M, K ↔ N, L ↔ O, so corresponding angles are equal.