Triangles with Non Congruent Sides

We have shown that in an isosceles triangle, the angles opposite the congruent sides are congruent. This was the Isosceles Triangle Theorem which we proved two weeks ago.

In this post, we are gong to learn a slightly related theorem: a theorem that states that if in a triangle, two sides are not congruent, then the angles opposite these sides are not congruent and the angle opposite to the larger side is the larger angle.

 triangle

In the triangle above, $latex \overline{AB}$ is greater than $latex \overline{BC}$. We will show that they are not equal and $latex \angle C > \angle B$. Continue reading