Question

use the given information to prove that ( \triangle rst cong \triangle vut ).
given: ( overline{rt} cong overline{vt} )
( angle rst cong angle vut )
prove: ( \triangle rst cong \triangle vut )

Explanation:

Step1: Identify vertical angles

$\angle RTS\cong\angle VTU$ (Vertical angles are congruent)

Step2: Apply AAS congruence criterion

In $\triangle RST$ and $\triangle VUT$, we have $\angle RST\cong\angle VUT$ (given), $\angle RTS\cong\angle VTU$ (vertical angles), and $\overline{RT}\cong\overline{VT}$ (given). By the AAS (Angle - Angle - Side) congruence criterion, $\triangle RST\cong\triangle VUT$.

Answer:

$\triangle RST\cong\triangle VUT$ by AAS congruence.