Question

Is MNL ≅ QNL? Why or why not?

A. Yes, they are congruent by either ASA or AAS.
B. Yes, they are both right triangles.
C. No, M is not congruent to NLQ.
D. No, there are no congruent sides.

Answer 1

A

Explanation:

Answer 2

The Angle Angle Side postulate (AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

The Angle Side Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Consider two right triangles MNL and QNL. Note that

1. In triangle MNL, m∠NLM=90°-m∠LMN=90°-58°=32°.

2. In triangle QNL, m∠NQL=90°-m∠QLN=90°-32°=58°.

In these triangles:

1. m∠MNL=m∠QNL=90° (given);
2. m∠NLM=m∠NQL=58° (proved);
3. m∠MLN=m∠QLN=32° (proved);
4. Side LN is common (given).

Then triangles MNL and QNL are congruent by ASA (1, 3 and 4 conditions) or by AAS (2, 3 and 4 conditions).

Answer: correct choice is A