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How do I solve this?​

How do I solve this?​-example-1
User Temple
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1 Answer

4 votes

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.

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.

User Allexiusw
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