Question

Triangle ABC. Line passes through points D, B, and E.

Given: ΔABC

Prove: All three angles of ΔABC add up to 180°.

The flowchart with missing reason proves the measures of the interior angles of ΔABC total 180°:

Top path, by Construction, line segment DE is parallel to line segment AC. By Alternate Interior Angles, angle EBC is congruent to angle BCA. By Substitution, the sum of the measures of angles BCA, CBA, and BAC equals 180 degrees. Next path, by Construction, line segment DE is parallel to line segment AC. By Alternate Interior Angles, angle DBA is congruent to angle BAC. By Substitution, the sum of the measures of angles BCA, BCA, and BAC equals 180 degrees. Next path, by Construction, line segment DE is parallel to line segment AC. By Definition of a Straight Angle, the measure of angle EBD equals 180 degrees. By Substitution, the sum of the measures of angles EBC, CBA, and DBA equals 180 degrees. Bottom path, by Construction, line segment DE is parallel to line segment AC. By space labeled 1, the sum of the measures of angles EBC, CBA, and DBA equals the measure of angle EBD. By Substitution, the sum of the measures of angles EBC, CBA, and DBA equals 180 degrees.

Which reason can be used to fill in the numbered blank space? (2 points)
Associative Property of Addition
Triangle Exterior Angle Theorem
Angle Addition Postulate
Commutative Property of Addition

Answer 1

DE is parallel to AC.

The second step assumes that the measured ∠DBA agrees with ∠BAC measured.

Alternating interior angles are angles formed by transverse lines inside parallel lines on alternating sides.

According to the alternating interior angle theorem, the alternating interior angles are equal.

The correct option is D. Theorem on alternative interior angles.

Answer 2

The reason that can be used to fill in the numbered blank space is the Angle Addition Postulate.