Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees. Is TriangleMNL ≅ TriangleQNL? Why or why not? A: Yes, they are congruent by either ASA or AAS.
B: Yes, they are both right triangles.
C: No, AngleM is not congruent to AngleNLQ.
D: No, there are no congruent sides.

Both triangles are congruent using either ASA or AAS Congruence Theorem. Therefore the right answer is: A: Yes, they are congruent by either ASA or AAS

Recall:

If two triangles are congruent by the ASA Congruence Theorem, they have two pairs of congruent angles and a pair of congruent included side.
If two triangles are congruent by the AAS Congruence Theorem, they have two pairs of congruent angles and a pair of congruent non-included side.

Triangle LMQ is shown in the image attached below.

Thus,

Proving Triangle MNL ≅ triangle QNL by ASA:

Triangle MNL and triangle QNL have two pairs of congruent angles: <LNM ≅ LNQ and <MLN and <QLN

Also they share a common side: side LN (included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

Proving Triangle MNL ≅ triangle QNL by AAS:

Triangle MNL and triangle QNL have two pairs of congruent angles: <LNM ≅ LNQ and <NML and <NQL

Also they share a common side: side LN (non-included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

In summary, both triangles are congruent using either ASA or AAS Congruence Theorem. Therefore the right answer is: A: Yes, they are congruent by either A: Yes, they are congruent by either ASA or AAS

Learn more about the ASA and AAS Congruence Theorem on:

https://brainly.com/question/2102943