# 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

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.

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mhalmantus

Given figure is:

Sum of angles in a triangle is ${180}^{\circ }$.
$In\mathrm{△}TPR$
${50}^{\circ }+{60}^{\circ }+\mathrm{\angle }TRP={180}^{\circ }$
$\mathrm{\angle }TRP={70}^{\circ }$
Step 4
$In\mathrm{△}TSR$,
${60}^{\circ }+{70}^{\circ }+\mathrm{\angle }TRP={180}^{\circ }$
$\mathrm{\angle }TRP={50}^{\circ }$
$In\mathrm{△}TRP\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}TSR$,
$\mathrm{\angle }TPR=\mathrm{\angle }TSR\left(Each{60}^{\circ }\right)$
$\mathrm{\angle }PTR=\mathrm{\angle }STR\left(Each{50}^{\circ }\right)$
TR=TR (Common)
Therefore, $\mathrm{△}TPR\stackrel{\sim }{=}\mathrm{△}TSR$ (BY AAS-congruence rule)/
Hence, both triangles are congruent.