Question

∠hei ≅ ∠ehi and overleftrightarrow{fg} || overleftrightarrow{eh}. complete the proof that ∠f ≅ ∠g.
1 ∠hei ≅ ∠ehi given
2 overleftrightarrow{fg} || overleftrightarrow{eh} given
3 ∠hei ≅ ∠g alternate interior angles theorem
4 ∠f ≅ ∠ehi
5 ∠hei ≅ ∠f transitive property of congruence
6 ∠f ≅ ∠g transitive property of congruence

Explanation:

Step1: Alternate Interior Angles Theorem

When two parallel lines (\(\overleftrightarrow{FG}\parallel\overleftrightarrow{EH}\)) are cut by a transversal, alternate - interior angles are congruent. For \(\angle F\) and \(\angle EHI\), the transversal is the line that intersects \(\overleftrightarrow{FG}\) and \(\overleftrightarrow{EH}\). So, the reason for \(\angle F\cong\angle EHI\) is the Alternate Interior Angles Theorem.

Answer:

Alternate Interior Angles Theorem