Question

1. in the figure, ∠1 = ∠2, ∠3 = ∠4, and tk = tl. you can justify the conclusion that △tks = △tlr by the

aas theorem.

sas postulate.

asa postulate.

sss postulate.

Explanation:

Step1: Recall triangle - congruence postulates

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. The SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. The ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. The SSS (Side - Side - Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze given information

We are given that $\angle1=\angle2$, $\angle3 = \angle4$, and $\overline{TK}=\overline{TL}$. Here, we have two pairs of angles and a non - included side.

Answer:

A. AAS Theorem