Question

1. given: ∠1≅∠2, ∠3≅∠4, (overline{ts}congoverline{tr}). name the postulate or theorem you can use to prove (\triangle tkscong\triangle tlr). sas postulate hl theorem aas theorem asa postulate

Explanation:

Step1: Recall triangle - congruence postulates and theorems

The SAS (Side - Angle - Side) postulate requires two sides and the included angle to be congruent. The HL (Hypotenuse - Leg) theorem is for right - triangles. The AAS (Angle - Angle - Side) theorem requires two angles and a non - included side to be congruent. The ASA (Angle - Side - Angle) postulate requires two angles and the included side to be congruent.

Step2: Analyze the given information

We are given that $\angle1\cong\angle2$, $\angle3\cong\angle4$, and $\overline{TS}\cong\overline{TR}$. In $\triangle TKS$ and $\triangle TLR$, we have two pairs of angles ($\angle1\cong\angle2$ and $\angle3\cong\angle4$) and a non - included side ($\overline{TS}\cong\overline{TR}$).

Answer:

C. AAS Theorem