Question

How do I solve this?​

Answer 1

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.