Please help! Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.

I constructed line AD as a perpendicular bisector of line BC. Angles BDA and CDA are both 90 degrees because of the construction of a perpendicular bisector. Angles BDA and CDA are congruent because of the transitive property of equality.  Line BD is also equal to CD according to the definition of a perpendicular bisector. Triangles ABD and ACD are congruent by the angle side angle postulate. Since the parts of the congruent triangles are congruent, lines AB and AC are congruent.

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

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