NCERT Solutions | Class 7 Maths Chapter 10 | Practical Geometry

CBSE Solutions | Maths Class 7

Check the below NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Pdf free download. NCERT Solutions Class 7 Maths were prepared based on the latest exam pattern. We have Provided Practical Geometry Class 7 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 7 Maths

NCERT Solutions Class 7 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	7th
Subject:	Maths
Chapter:	10
Chapters Name:	Practical Geometry
Medium:	English

Practical Geometry | Class 7 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 7 Maths Chapter 10 Practical Geometry to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 7 Maths Chapte 10 Practical Geometry Exercise 10.1

Ex 10.1 Class 7 Maths Question 1.

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

Solution:

Steps of Construction :

Take any point P on the line AB.
Take any point C outside AB and join CP.
With P as centre, draw an arc cutting AB and PC at X and Y respectively.
With centre C and the same radius as in step 3, draw an arc on the opposite side of the PC to cut the PC at Q.
With centre Q and radius equal to XY, draw an arc cutting the arc drawn in step 4 at R.
Join CP and produce it in both directions to obtain the required line.

Ex 10.1 Class 7 Maths Question 2.

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.

Solution:

Steps of Construction:

Draw a line l and take any point P on it.
With P as centre and any radius, draw an arc to intersect line l at A and B.
With A as centre and radius greater than PA, draw in an arc.
With centre B and the same radius, as in step 2, draw another arc to intersect the arc drawn in step 2 at C.
Join PC and produce it to Q. Then PQ ⊥ l
With P as centre and radius equal to 4 cm, draw an arc to intersect PQ at X such than PX = 4 cm.
At X, make ∠RXP = ∠BPX.
Join XR to obtain the required line m.

Validity: Since ∠BXP = ∠BPX and these are alternate angles, therefore, .XR || l, i.e., m || l and contain X such that PX = 4 cm and ∠XPB = 90°.

Ex 10.1 Class 7 Maths Question 3.

Let l be a line and P be a point 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?

Solution:

Steps of Construction :

Draw a line l and take any point P outside it.
Take any point Q on line l.
Join PQ.
With a centre, draw an arc cutting l and PQ at C and D respectively.
With centre P and the same radius as in step 4, draw an arc on the opposite side of PQ to cut PQ at E.
With centre E and radius equal to CD,’ draw an arc cutting the arc of step 5 at F.
Join PF and produce it in both directions to obtain the required line m.
Take any point R on m.
Through P, draw a line PS || PQ by following the steps already explained.
The shape of the figure endorsed by these lines is a parallelogram RPQS.

NCERT Solutions for Class 7 Maths Chapte 10 Practical Geometry Exercise 10.2

Ex 10.2 Class 7 Maths Question 1.

Construct ∆XYZ in which XY = 45 cm, YZ = 5 cm and ZX = 6 cm.

Solution:

Steps of Construction :

Draw a line segment YZ = 5 cm.
With Y centre and draw an arc radius cm.
With Z as centre and draw another arc intersecting the arc radius = 6 cm, at X.
Join XY and XZ to obtain the required triangle.

Ex 10.2 Class 7 Maths Question 2.

Construct an equilateral triangle of side 5.5 cm.

Solution:

Steps of Construction :

Draw a line segment BC = 5.5 cm.
With centre B and radius = 5.5 cm, draw an arc.
With centre C and radius = 5.5 cm, draw another arc intersecting the arc drawn in step 2 at A.
Join AB and AC to obtain the required triangle.

Ex 10.2 Class 7 Maths Question 3.

Draw ∆PQR with PQ = 4, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

Solution:

Steps of Construction :

Draw a line segment QR = 3.5 cm.
With centre Q and radius = 4 cm, draw an arc.
With R as centre and radius = 4 cm, draw another arc intersecting the arc drawn in step 2 at P.
Join PQ and PR to obtain the required triangle. ∆PQR is an isosceles triangle.

Ex 10.2 Class 7 Maths Question 4.

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

Solution:

Steps of Construction :

Draw a line segment BC = 6 c.m
With centre B and radius = 2.5 cm, draw an arc.
With centre C and radius =6.5 cm, draw another arc intersecting the arc drawn in step 2 at A.
Join AB and AC to obtain the required triangle.
On measuring, we find that ∠B = 90°.

NCERT Solutions for Class 7 Maths Chapte 10 Practical Geometry Exercise 10.3

Ex 10.3 Class 7 Maths Question 1.

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

Solution:

Steps of Constipation :

Draw a line segmerit DE = 5cm.
Draw ∠EDX = 90°.
With centre D and radius = 3 cm, draw an are to intersect DX at F.
Join EF to obtain the required triangle DBF.

Ex 10.3 Class 7 Maths Question 2.

Construct an isosceles triangle in which the lengths of each of its equal Sides is 6.5 cm find the angle between them is 110°

Solution:

Steps of Construction :

Draw a line segment BC = 6.5 cm.
Draw ∠CBX = 110°.
With B as centre and radius = 6.5 cm, draw an arc intersecting BX at A.
Join AC to obtain the required ∆ABC.

Ex 10.3 Class 7 Maths Question 3.

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

Solution:

Steps of Construction :

Draw a line segment BC =7.5 cm.
Draw ∠BCX = 60°.
With C as centre and radius = 5 cm, draw an arc intersecting CX at A.
Join AB to obtain the required ∆ABC.

NCERT Solutions for Class 7 Maths Chapte 10 Practical Geometry Exercise 10.4

Ex 10.4 Class 7 Maths Question 1.

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

Solution:

Steps of Construction :

1. Draw a line segment AB = 5.8 cm.
2. Draw ∠BAX = 60°.
3. Draw ∠ABY, with Y on the same side of AB
such that ∠ABY = 30°.
Let AX and BY interest at C.
Then, ∆ABC is the required triangle.

Ex 10.4 Class 7 Maths Question 2.

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

Solution:

Here, we are given the side PQ, ∠Q and ∠R. But to draw the triangle, we require ∠P
NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry 11

Ex 10.4 Class 7 Maths Question 3.

Examine whether you can construct
∆DEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer.

Solution:

Since m∠E +m∠F = 110° + 80° = 190°, so the ∆DEF cannot be drawn as the’sum of all the angles of a triangle is 180°.

NCERT Solutions for Class 7 Maths Chapte 10 Practical Geometry Exercise 10.5

Ex 10.5 Class 7 Maths Question 1.

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

Solution:

Steps of Construction :

Draw a line segment QR = 8 cm.
Draw ∠XQR = 90°.
With R as centre and radius =10 cm, draw an arc to intersect ray QX at P.
Join RP to obtain the required ∆PQR.

Ex 10.5 Class 7 Maths 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 :

Draw a line segment QR = 4 cm.
Draw ∠XQR = 90°.
With R as centre and radius equal to hypotenuse 6 cm, draw an arc to intersect ray QX at P.
Join RP to obtain the required ∆PQR.