**Chapter 10 Practical Geometry Exercise 10.5**

Question 1.

Construct the right angled ∆PQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm.

Solution:

Steps of construction:

(i) Draw QR = 8 cm.

(ii) Draw m∠Q = 90°.

(iii) Draw an arc with centre R and radius 10 cm to cut the perpendicular line at P.

(iv) ∆PQR is the required triangle.

[Using RHS criterion]

Question 2.

Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

Solution:

Steps of construction:

(i) Draw AB = 4 cm.

(ii) Draw ∠A = 90°.

(iii) Cut BC = 6 cm.

(iv) ∆CAB is the required right-angled triangle.

[Using RHS criterion]

Question 3.

Construct an isosceles right-angled triangle ABC, where m∠ACB = 90° and AC = 6 cm.

Solution:

Steps of construction:

(i) Draw AC = 6 cm.

(ii) Draw ∠A =∠C = 45° to meet each other at B such that m∠B = 90°.

(iii) ∆ABC is right-angled isosceles triangle which is the required triangle.

[Using RHS criterion]