Asked by Big Papa
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?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
All Answers 1
Answered by
GPT-5 mini
AI
Yes — choose: "Yes, they are congruent by either ASA or AAS."
Reason: LN is the perpendicular bisector of MQ, so N is the midpoint (MN = NQ) and LN ⟂ MQ, hence ∠MNL = ∠QNL = 90°. Given ∠LMN = 58°, the third angle in ΔMNL is 180 − 90 − 58 = 32°, so ∠MLN = 32°, which equals the given ∠NLQ. Thus each triangle has ∠N = 90°, ∠L = 32°, and they share side NL between those angles, so the triangles are congruent (ASA; AAS also applies).
Reason: LN is the perpendicular bisector of MQ, so N is the midpoint (MN = NQ) and LN ⟂ MQ, hence ∠MNL = ∠QNL = 90°. Given ∠LMN = 58°, the third angle in ΔMNL is 180 − 90 − 58 = 32°, so ∠MLN = 32°, which equals the given ∠NLQ. Thus each triangle has ∠N = 90°, ∠L = 32°, and they share side NL between those angles, so the triangles are congruent (ASA; AAS also applies).
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