A certain triangle has two angles that have the same measure. If the lengths of two of the sides of the triangle are 50 and 30, what is the least possible value for the perimeter of the triangle.

This uses the fact that if **two angles in a triangle are congruent, then two sides in the triangle are congruent**. So we have an isosceles triangle (two equal sides and a base.)

There are two ways to make this triangle isosceles. Side lengths {50, 50, 30} or {30, 30, 50}. In the second case, the perimeter will be smaller. P = 30 + 30 + 50 =
**110 **is smallest possible perimeter.