Prove: the sum of the interior angle measures of labc is 180°, statement reason 1. let points a, b, and cform a triangle given 2. let de be a line passing through b, parallel to ac, with angles as labeled defining a parallel line and labeling angles 4. m21 = m24, and m23 = m25. congruent angles have equal measures. 5. m24+ m22 - m25 = 180° angle addition and definition of a straight angle 6. m21 - m42 - m23 = 180° substitution what is the missing step in this proof?
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°.