Question

use the given information to prove that ( \triangle pqr cong \triangle tsr ).
given: ( overline{qr} cong overline{sr} )
( overline{pr} cong overline{tr} )
prove: ( \triangle pqr cong \triangle tsr )

Explanation:

Step1: Identify vertical angles

$\angle PRQ\cong\angle TRS$ (Vertical angles are congruent)

Step2: Apply SAS (Side - Angle - Side) congruence criterion

In $\triangle PQR$ and $\triangle TSR$:

• $\overline{QR}\cong\overline{SR}$ (Given)
• $\angle PRQ\cong\angle TRS$ (Vertical angles)
• $\overline{PR}\cong\overline{TR}$ (Given)

By the SAS (Side - Angle - Side) congruence criterion, $\triangle PQR\cong\triangle TSR$

Answer:

$\triangle PQR\cong\triangle TSR$ by the SAS (Side - Angle - Side) congruence criterion.