Question

1. given: ∠d≅∠t, ∠e≅∠u, eo≅ux name the postulate or theorem you can use to prove the triangles congruent. asa postulate sss postulate sas postulate aas theorem

Explanation:

Step1: Recall congruence postulates and theorems

The ASA (Angle - Side - Angle) postulate requires two pairs of congruent angles and the included side congruent. The SSS (Side - Side - Side) postulate requires all three sides of one triangle congruent to the corresponding three sides of the other triangle. The SAS (Side - Angle - Side) postulate requires two pairs of congruent sides and the included angle congruent. The AAS (Angle - Angle - Side) theorem requires two pairs of congruent angles and a non - included side congruent.

Step2: Analyze given information

We are given $\angle D\cong\angle T$, $\angle E\cong\angle U$, and $\overline{EO}\cong\overline{UX}$. Here we have two pairs of congruent angles and a non - included side congruent.

Answer:

D. AAS Theorem