Question

1. given: ∠1 ≅ ∠2, ∠3 ≅ ∠4, overline{ts} ≅ overline{tr} name the postulate or theorem you can use to prove △tks ≅ △tlr asa postulate aas theorem sas postulate hl theorem

Explanation:

Step1: Recall triangle congruence theorems

• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
• HL (Hypotenuse - Leg): For right - triangles, the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle.

Step2: Analyze the given information

We are given \(\angle1\cong\angle2\), \(\angle3\cong\angle4\), and \(\overline{TS}\cong\overline{TR}\).
In \(\triangle TKS\) and \(\triangle TLR\):

• The non - included side: \(\overline{TS}\cong\overline{TR}\) (given).
• Two angles: \(\angle1\cong\angle2\) and \(\angle3\cong\angle4\) (given).

Answer:

AAS Theorem