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Base Angle Theorem

From AoPSWiki

The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent.

Proof

Since the triangle only has three sides, the two congruent sides must be adjacent. Let them meet at vertex A.

Now we draw altitude AD to BC. From the Pythagorean Theorem, BD=CD, and thus \triangle ABD is congruent to \triangle ACD, and \angle DBA=\angle DCA. unitsize(5); defaultpen(fontsize(10));pair A,B,C,D,E,F,G,H;A=(0,10);B=(-5,0);C=(5,0);D=(0,0);E=(1,1);F=(-1,1);G=(-1,0);H=(1,0...

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