Question

in the figure, ∠1 ≅ ∠2, ∠3 ≅ ∠4 and (overline{tk}=overline{tl}). you can justify the conclusion that (\triangle tkscong\triangle tlr) by the

asa postulate

sas postulate

sss postulate

aas theorem

Explanation:

Step1: Recall congruence postulates

• 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.
• 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.
• SSS (Side - Side - Side): Three sides of one triangle are congruent to three sides 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.

Step2: Analyze given information

We are given that $\angle1\cong\angle2$, $\angle3\cong\angle4$ and $\overline{TK}=\overline{TL}$. The side $\overline{TK}$ is between $\angle1$ and $\angle3$, and the side $\overline{TL}$ is between $\angle2$ and $\angle4$. So we have two pairs of angles and the included side between them are congruent. This satisfies the ASA (Angle - Side - Angle) postulate.

Answer:

ASA Postulate