Question

Use the given information to prove that APQR ATSR. Check 1 R S P Statement LPQR LTSR 2 QR SR Validate 3 APQR ATSR Т Given: QR SR ZPQR LTSR Prove: APQR = ATSR Reason Given Given Send To Proof ✔ Send To Proof ✓ Send To Proof Reason?​

Answer 1

By the AAS congruence theorem,
`(\triangle PQR \cong \triangle TSR)`.

The given information is that
`(QR \cong SR)`, and
`(\angle PQR \cong \angle TSR)`. We need to prove that
`(\triangle PQR \cong \triangle TSR)`.

To prove that
`(\triangle PQR \cong \triangle TSR)`, we can use the AAS congruence theorem. According to the AAS congruence postulate (we have two pairs of congruent angles and the included side congruent) Therefore, we have proven that ΔPQR ≅ ΔTSR.

Statement: Reason

`(QR \cong SR)` (Given)

`(\angle PQR \cong \angle TSR)` (Given)

∠PRT ≅ ∠ QRS Vertical Angles Property

`(QR \cong SR)` (Given)

`(\triangle PQR \cong \triangle TSR)` AAS Congruence Property.