Linking Triangle Angle Sum and Inscribed Angle Theorems

We have shown that the angle sum of a triangle is $latex 180^\circ$. We have also shown that the measure of an inscribed angle is half the measure the central angle that intercepts the same arc. In this post, we use the Inscribed Angle Theorem to show that the Triangle Angle Sum Theorem holds.

central-angle

Theorem

The angle sum of a triangle is $latex 180^\circ$.

Proof

Consider the figures above. In the first figure, the triangle is divided into three central angles. Clearly the three angles add up to a complete rotation about the center so  Continue reading