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 and triangle gfh, with f being a common point on the line dg, and de parallel to gh)
then a table with columns statements and reasons for filling in the proof steps.

Explanation:

Step1: State given parallel lines

$\overline{DE} \parallel \overline{GH}$

Step2: Identify alternate interior angles

$\angle D \cong \angle G$, $\angle E \cong \angle H$

Step3: 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 (for parallel lines cut by a transversal)
$\triangle DFE \sim \triangle GFH$	AA (Angle-Angle) Similarity Postulate