# NCERT Solutions for Class 7 Maths Chapter 10

## Practical Geometry Class 7

### Exercise 10.1 : Solutions of Questions on Page Number : 196

Q1 :

Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

The steps of construction are as follows.

(i)Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P. (ii)Taking P as centre and with a convenient radius, draw an arc intersecting line AB at point D and PC at point E. (iii) Taking C as centre and with the same radius as before, draw an arc FG intersecting PC at H. (iv) Adjust the compasses up to the length of DE. Without changing the opening of compasses and taking H as the centre, draw an arc to intersect the previously drawn arc FG at point I. (v) Join the points C and I to draw a line 'l'. This is the required line which is parallel to line AB.

Q2 :

Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

The steps of construction are as follows.

(i) Draw a line l and take a point P on line l. Then, draw a perpendicular at point P. (ii) Adjusting the compasses up to the length of 4 cm, draw an arc to intersect this perpendicular at point X. Choose any point Y on line l. Join X to Y. (iii) Taking Y as centre and with a convenient radius, draw an arc intersecting l at A and XY at B. (iv) Taking X as centre and with the same radius as before, draw an arc CD cutting XY at E. (v)Adjust the compasses up to the length of AB. Without changing the opening of compasses and taking E as the centre, draw an arc to intersect the previously drawn arc CD at point F. (vi) Join the points X and F to draw a line m. Line m is the required line which is parallel to line l.

Q3 :

Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

### Exercise 10.2 : Solutions of Questions on Page Number : 199

Q1 :

Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Q2 :

Construct an equilateral triangle of side 5.5 cm.

Q3 :

Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of

triangle is this?

Q4 :

Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠ B.

### Exercise 10.3 : Solutions of Questions on Page Number : 200

Q1 :

Construct ΔDEF such that DE = 5 cm, DF = 3 cm and m∠ EDF = 90°.

Q2 :

Construct an isosceles triangle in which the lengths of each of its equal sides

is 6.5 cm and the angle between them is 110°.

Q3 :

Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m∠ C = 60°.

### Exercise 10.4 : Solutions of Questions on Page Number : 202

Q1 :

Construct ΔABC, given m∠ A = 60°, m∠ B = 30° and AB = 5.8 cm.

Q2 :

Construct ΔPQR if PQ = 5 cm, m∠ PQR = 105° and m∠ QRP = 40°.

(Hint: Recall angle sum property of a triangle).

Q3 :

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠ E =

### Exercise 10.5 : Solutions of Questions on Page Number : 203

Q1 :

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

Q2 :

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

Q3 :

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