## EXERCISE 10.5

#### Page No 203:

#### Question 1:

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

#### Answer:

A rough sketch of ΔPQR is as follows.

The steps of construction are as follows.

(i) Draw a line segment QR of length 8 cm.

(ii) At point Q, draw a ray QX making 90º with QR.

(iii) Taking R as centre, draw an arc of 10 cm radius to intersect ray QX at point P.

(iv) Join P to R. ΔPQR is the required right-angled triangle.

#### Question 2:

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

#### Answer:

A right-angled triangle ABC with hypotenuse 6 cm and one of the legs as 4 cm has to be constructed. A rough sketch of ΔABC is as follows.

The steps of construction are as follows.

(i) Draw a line segment BC of length 4 cm.

(ii) At point B, draw a ray BX making an angle of 90º with BC.

(iii) Taking C as centre, draw an arc of 6 cm radius to intersect ray BX at point A.

(iv) Join A to C to obtain the required ΔABC.

#### Question 3:

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

#### Answer:

In an isosceles triangle, the lengths of any two sides are equal.

Let in ΔABC, AC = BC = 6 cm. A rough sketch of this ΔABC is as follows.

The steps of construction are as follows.

(i) Draw a line segment AC of length 6 cm.

(ii) At point C, draw a ray CX making an angle of 90º with AC.

(iii) Taking point C as centre, draw an arc of 6 cm radius to intersect CX at point B.

(iv) Join A to B to obtain the required ΔABC.