Inscribed Angles of a Circle Theorem

Consider two inscribed angles $\angle ADB$ and $\angle ACB$ that intercept the same arc $\overgroup{AB}$ in a circle.

By the Inscribed Angle Theorem, the measures of $\angle ADB$ and $\angle ACB$ are half the measure of $\overgroup{AB}.$ Therefore, by the Transitive Property of Equality, it can be said that these two angles have the same measure. Consequently, by the definition of congruent angles, $\angle ADB$ and $\angle ACB$ are congruent.