Choose case when the triangles are similar.
A) $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$
B) $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$
C) $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$
D) $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$

Question

Choose case when the triangles are similar. 
A) $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$ 
B) $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$ 
C) $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$ 
D) $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$

Quizplus · Accepted Answer

In choice B, two angles of one triangle ($\angle A$ and $\angle M$) are equal to two angles of another triangle ($\angle A$ and $\angle M$), and the corresponding sides ($AB:AM$ and $AC:MK$) are in the same ratio ($99:117=110:130$). This satisfies the criteria for similarity of triangles. None of the other choices have similar triangles.

Choose Case When the Triangles Are Similar ∠A=35∘\angle A = 35 ^ { \circ }∠A=35∘

Choose Case When the Triangles Are Similar $\angle A = 35 ^ { \circ }$