Question

How do I solve this?​

Answer 1

Answer:

The given parameters are;

$\overline{PS}$ ≅ $\overline{PT}$, ∠PRS ≅ ∠PRT

To prove that ΔPRS ≅ ΔPRT

A two column proof is given as follows;

Statement                 ${}$                   Reason

∠PRS and  ∠PRT are ≅   ${}$            Given

∠PRS and ∠PRT are     ${}$               ∡ that form a linear pair are supplementary

supplementary angles

∠PRS and ∠PRT are right ∡   ${}$  Two ≅ and supplementary angles are right ∡

ΔPRS and ΔPRT are right Δ   ${}$  Triangle with one angle = 90°

$\overline {PS}$ ≅ $\overline {PT}$                ${}$                    Given

$\overline {PR}$ ≅ $\overline {PR}$                ${}$                    Reflective property

ΔPRS ≅ ΔPRT             ${}$               By hypotenuse leg postulate.

Step-by-step explanation:

The given parameters are;

$\overline{PS}$ ≅ $\overline{PT}$, ∠PRS ≅ ∠PRT

To prove that ΔPRS ≅ ΔPRT

A two column proof is given as follows;

Statement                 ${}$                                              Reason

∠PRS and  ∠PRT are congruent        ${}$                   Given

2) ∠PRS and ∠PRT are supplementary angles by angles that form a linear pair are supplementary

3) ∠PRS and ∠PRT are right angles by   ${}$  Two congruent angles which are also supplementary (sum up to 180°) are two 90° angles

4) ΔPRS and ΔPRT are right triangles   ${}$  Triangle with one angle = 90°

$\overline {PS}$ ≅ $\overline {PT}$                ${}$                    Given

$\overline {PR}$ ≅ $\overline {PR}$                ${}$                    Reflective property

ΔPRS ≅ ΔPRT             ${}$               By hypotenuse leg postulate for the congruency of two right triangles.