Question

Which of the following relation is correct if PQ = PS, PR = PT and ∠QPS = ∠TPR?

- QR = ST
- QR > ST
- QR < ST
- QR = QP

Hint:

### If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

## The correct answer is: QR = ST

### As it is given that, PQ = PS, PR = PT and ∠QPS = ∠TPR,

Here, two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle.

So, ∆ PQR is congruent to Δ PST by SAS congruence rule.

Hence, QR = ST (Corresponding parts of congruent triangles).

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