Question

in the diagram below, segments $overline{tu}$ and $overline{qs}$ perpendicularly bisect each other at point r. which of the following can be used to prove that $\triangle qrtcong\triangle sru$?
○ asa
○ sas
○ sss
○ hl

Explanation:

Step1: Identify given information

Segments $\overline{TU}$ and $\overline{QS}$ perpendicularly bisect each other at $R$. So, $TR = UR$, $QR=SR$, and $\angle QRT=\angle SRU = 90^{\circ}$.

Step2: Recall congruence - criteria

We have two - sides and the included angle of one triangle equal to two - sides and the included angle of another triangle.
In $\triangle QRT$ and $\triangle SRU$, $QR = SR$, $\angle QRT=\angle SRU$, and $TR = UR$.

Step3: Determine congruence postulate

By the Side - Angle - Side (SAS) congruence postulate, $\triangle QRT\cong\triangle SRU$.

Answer:

B. SAS