The missing step in this two-column proof include the following: C. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5. Reason: Alternate Interior Angles Theorem.
In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
In this context, a two-column proof that proves that the sum of the interior angle measures of ΔABC is 180° should be completed as follows;
Statement Reason_________________
1. Points A, B, and C form a triangle. 1. Given
2. Let DE be a line passing through B 2. Definition of parallel lines.
and parallel to AC.
3. ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3. Alternate Interior Angles Theorem
4. m∠1 = m∠4 and m∠3 = m∠5 4. Definition of congruent angles
5. m∠4 + m∠2 + m∠5 = 180° 5. Angle addition and definition of a straight line
6. m∠1 + m∠2 + m∠3 = 180° 6. Substitution