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.
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
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