Honors Question

Question

Explain why it is not possible to draw a triangle that has two equal sides but not two equal angles?

Answer 1

A triangle that has two equal sides is an isosceles triangle. From the vertex where the two equal sides meet draw the height of the isosceles triangle. This line segment divides the isosceles triangle into two congruent right triangles. This can be proven. If two triangles are congruent, there are three pairs of congruent angles. The three pairs are the two right angles, the two angles on each side of the height at the vertex where the two equal sides meet, and the two angles that are opposite the equal sides. In congruent triangles, corresponding parts (angles and segments) are congruent.