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olga2289 [7]
2 years ago
6

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.

Mathematics
1 answer:
luda_lava [24]2 years ago
4 0

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

<h3>What is ASA Congruence Theorem?</h3>

The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.

The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.

Triangle LMQ is shown in the figure attached below.

Thus, Proving

Triangle MNL ≅ triangle QNL (ASA)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <MLN and <QLN

Also, they have a common side: side LN (included side).

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

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 have a common side: side LN (non-included side).

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

Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.

Learn more about the ASA and AAS Congruence Theorem on:

brainly.com/question/2102943

#SPJ1

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