If a triangle has two angles congruent, then two sides are congruent

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If a triangle has two angles congruent, then two sides are congruent. How can this be proven without using ASA. I have been trying to solve this but I keep ending up having to use ASA. I was wondering if anyone had any idea how to do it.

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2 Answers

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It follows from Law of sines

$\frac {a}{sin A}=\frac {b}{sin B}=\frac {c}{sin C} = 2 R$

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Draw a median from vertex which is also a vertex of non-congruent angle. This median is also an altitude and you have two congruent triangles by SAS (half of the side, right angle and altitude which is a common side for both triangles).

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