Chapter 5.3, Problem 57SPR

To determine

Toprove:Thetriangle $\Delta SRT\cong \Delta QRT$ .

Explanation of Solution

Given information:

The given figure is

  

The sides $\overline{SR}\cong \overline{QR}$ and $T$ is the midpoint of $\overline{SQ}$ .

Prove:

It is given that $T$ is the midpoint of $\overline{SQ}$ .

Thus, the segment $\overline{ST}\cong \overline{QT}$ .

Since,

  $\overline{SR}\cong \overline{QR}$ (given)

  $\overline{ST}\cong \overline{QT}$

And $\angle RTS\cong \angle RTQ=90°$

Thus, by Side-side-angle criteria for congruency,

  $\Delta SRT\cong \Delta QRT$ .

Hence, proved.