Question

name: date period
②
△pie≌△____ by ____

Explanation:

Step1: Analyze the given information

We know that in the figure, \(PE = ET\) (marked as equal on the line segment \(PT\)), \(\angle P=\angle T\) (marked as equal angles), and \(\angle PEP=\angle TEA\) (vertical angles are equal).

Step2: Use the ASA (Angle - Side - Angle) congruence criterion

The ASA congruence criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle PIE\) and \(\triangle TAE\), \(\angle P=\angle T\), \(PE = ET\), \(\angle PEP=\angle TEA\)

Answer:

\(\triangle PIE\cong\triangle TAE\) by \(ASA\)