Question

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 space labeled 1, 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 Angle Addition Postulate, 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?

Answer 1

Answer:

Alternate interior angles.

Step-by-step explanation:

We have been asked to find the missing reason of flowchart, which proves that the measure of interior angles of ΔABC is 180°.

We have been given that by Construction, line segment DE is parallel to line segment AC and we can see line AB as a transversal.

Since we know that angles formed by inside of two parallel lines and opposite side a transversal are known as alternate interior angles.

We can see that angle DBA and BAC are formed inside parallel line segments DE and AC and opposite side of line segment AB. Therefore, angle DBA and BAC are congruent by alternate interior angles.

Answer 2

The actual answer is Substitution

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