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 option B, we have two pairs of congruent angles ($\angle A$ and $\angle M$, and $\angle B$ and $\angle K$), and the sides are in proportion ($\frac{AB}{AC} = \frac{99}{110}$ and $\frac{MN}{MK} = \frac{117}{130}$). This satisfies the criteria for similarity, which states that corresponding angles are congruent and corresponding sides are in proportion. Therefore, the triangles are similar. The other options do not have enough information to determine similarity.

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

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