Question

Suppose a triangle has two angles that are equal. Show the two sides opposite these two angles are also equal.

Answer 1

Drawn triangle ABC. Angle BAC is equal to angle BCA. Draw segment BD. BD is an angle bisector of angle ABC.

Since segment BD is an angle bisector of angle ABC, then angle ABD equals CBD.

Segment BD of triangle ABD is congruent the segment BD of triangle CBD, reflexive property.

From the ASA property, triangle ABD is congruent to triangle CBD.

Therefore, side AB equals side BC, corresponding parts of congruent triangles are equal (CPCTC)

Answer 2

I forgot to show that angle BDA is congruent to BDC.

Show that 180-(BAC+ABD)= BDA Definition of a triangle ( sum of the angles =180 degrees.

Show that 180-(DBC+BCA)= BDC Definition of a triangle

BDC=BDA Substitution (ABD congruent to DBC, BAC congruent to BCA)