Question

Select the correct answer. Given: ABC Prove: The sum of the interior angle measures of ABC is 180°

Answer 1

We can prove this by doing a statement and reason (more or less). The first thing we need to do is a construction of segment OG which is parallel to BC and touches A. Since it forms a straight line, we can say that m<OAB + m<A + m<GAC is equal to 180° (because it is a straight line). But, by alternate interior angles theorem, we can say that m<B = m<OAB and m<C = m<GAC. Therefore, by transitivity, m<A + m<B + m<C = 180°. Since angles A, B, and C are the interior angles of triangle ABC, we proved that the sum of the interior angles of ABC is 180°.