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°.

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