Decide whether the two triangles must be congruent. If so, write the congruence and name the postulate used. If not. write no congruence can be deduced.12210203482.jpg

Given figure is:

Sum of angles in a triangle is ${\displaystyle {180}^{\circ }}$.
${\displaystyle In\mathrm{△}TPR}$
${\displaystyle {50}^{\circ }+{60}^{\circ }+\mathrm{\angle }TRP={180}^{\circ }}$
${\displaystyle \mathrm{\angle }TRP={70}^{\circ }}$
Step 4
${\displaystyle In\mathrm{△}TSR}$,
${\displaystyle {60}^{\circ }+{70}^{\circ }+\mathrm{\angle }TRP={180}^{\circ }}$
${\displaystyle \mathrm{\angle }TRP={50}^{\circ }}$
${\displaystyle In\mathrm{△}TRP\text{and}\mathrm{△}TSR}$,
${\displaystyle \mathrm{\angle }TPR=\mathrm{\angle }TSR\left(Each{60}^{\circ }\right)}$
${\displaystyle \mathrm{\angle }PTR=\mathrm{\angle }STR\left(Each{50}^{\circ }\right)}$
TR=TR (Common)
Therefore, ${\displaystyle \mathrm{△}TPR\stackrel{\sim }{=}\mathrm{△}TSR}$ (BY AAS-congruence rule)/
Hence, both triangles are congruent.