Describing Triangles

Consider the given diagram.

We see that two sides in a triangle are congruent. According to the base angles theorem the angles opposite these sides are congruent. By the theorem we know that $\angle A$ $\cong$ $\angle C.$ Therefore, these two angles have the same measure.

Next, we know by the interior angles theorem that the sum of the measures of the interior angles of a triangle equals $180^{\circ }.$

Consider the given diagram. Note that $\overline{AB}$ $\cong$ $\overline{BC}$ and therefore $△ABC$ is an isosceles triangle. The triangle's vertex angle, $\angle ABC,$ is bisected by $\overline{BO}.$

For the triangle $ABC$ we can apply the base angles theorem. Thus, $\angle A\cong \angle C$ and they must have the same measure.