Question

In the following figure, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is ______.

Options

• a right triangle but not isosceles

• an isosceles right triangle

• isosceles but not a right triangle

• neither isosceles nor right triangle

Answer 1

In the following figure, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is an isosceles right triangle.

Explanation:

Since, PQ Perpendicular to RQ

So, ∆PQR = 90°

∴ ∆PQR is right-angled triangle.

Also, in ΔPQR,

PQ = QR

ΔPQR is an isosceles triangle.

Hence, ΔPQR is an isosceles right-angled triangle.