Question

1. what is the reason for step 5 in this proof? a. vertical angles theorem b. opposite interior angles of a parallelogram are congruent c. all angles of a rectangle have the same measure d. alternate interior angles theorem

Explanation:

• In a parallelogram \(DEFG\) with \(DG\parallel EF\), when a transversal (in this case, the lines formed by the intersection of \(DF\) and \(GE\)) cuts two parallel lines, the alternate interior angles are congruent.
• For \(\angle HGD\) and \(\angle HEF\), since \(DG\parallel EF\) and \(GE\) is a transversal, by the Alternate Interior Angles Theorem, \(\angle HGD\cong\angle HEF\). Similarly, for \(\angle HDG\) and \(\angle HFE\), since \(DG\parallel EF\) and \(DF\) is a transversal, by the Alternate Interior Angles Theorem, \(\angle HDG\cong\angle HFE\).

Answer:

D. Alternate Interior Angles Theorem