# NCERT solution class 7 chapter 10 Practical geometry exercise 10.5 mathematics

## EXERCISE 10.5

#### Question 1:

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

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.

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.

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. error: Content is protected !! 