Question

Question 16
In the given figure, PQ$\perp$RQ, PQ = 5 cm and QR = 5 cm. Then, $△PQR$ is



a) a right-angled triangle but not isosceles
b) an isosceles right-angled triangle
c) isosceles but not a right-angled triangle
d) neither isosceles nor right-angled triangle

Answer 1

Given : PQ$\perp$RQ, PQ = 5 cm and QR = 5 cm

Since, PQ$\perp$RQ

So, $\angle$ PQR = ${90}^{\circ }$

$\therefore △$ PQR is a right angled triangle.

Also, in $△$PQR,

PQ = QR

$\therefore △$ PQR is an isosceles triangle.

Hence, $△$ PQR is an isosceles right-angled triangle.