MCQ
In figure, $PS = QR$ and $\angle\text{SPQ} = \angle\text{RQP}.$ Then
- ✓$PR = QS$
- B$PR > QS$
- C$PR ≤ QS$
- D$PR < QS$
✓
Answer
Correct option: A.
$PR = QS$
In $\triangle\text{QPR}$ and $\triangle\text{PQS},$
$QR = PS$ (Given)
$\angle\text{RQP} = \angle\text{SPQ}$ (Given)
$PQ = PQ$ (Common)
$\therefore \triangle\text{QPR} ≅ \triangle\text{PQS}$ (SAS Axio)
$\therefore PR = QS (C.P.C.T.)$
$QR = PS$ (Given)
$\angle\text{RQP} = \angle\text{SPQ}$ (Given)
$PQ = PQ$ (Common)
$\therefore \triangle\text{QPR} ≅ \triangle\text{PQS}$ (SAS Axio)
$\therefore PR = QS (C.P.C.T.)$
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