Question

directions: complete each proof.

1. given: $overline{de} \parallel \overline{gh}$

prove: $\triangle dfe \sim \triangle gfh$
(there is a diagram with triangle dfe, point f on dg, and triangle gfh, with de parallel to gh)
(a table with statements and reasons columns, with some filled entries: de || gh (given); $\angle d \cong \angle g$, $\angle e \cong \angle h$ (alternate interior angles theorem), and empty rows below)

Explanation:

Step1: State vertical angles congruence

$\angle DFE \cong \angle GFH$

Step2: Apply AA similarity criterion

$\triangle DFE \sim \triangle GFH$

Answer:

Statements	Reasons
$\angle D \cong \angle G$, $\angle E \cong \angle H$	Alternate Interior Angles Theorem
$\angle DFE \cong \angle GFH$	Vertical Angles Congruence Theorem
$\triangle DFE \sim \triangle GFH$	AA (Angle-Angle) Similarity Postulate