NCERT Solutions for Class 7 Maths Chapter 10 - Practical Geometry

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry. Furthermore, here we’ve provided you with the latest solution for Class 7 Maths Chapter 10 – Practical Geometry. As a result here you’ll find solutions to all the exercises. This NCERT Class 7 solution will help you to score good marks in your exam.

Students can refer to our solution for NCERT Class 7 Maths Chapter 10 – Practical Geometry. The Chapter 10 Solution of NCERT will help students prepare for the exams and easily crack the exam. Below we’ve provided you with the exercise-wise latest solution.

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Pdf Download

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Exercise Wise Solution

Exercise 10.1 – Page 196 of NCERT
Exercise 10.2 – Page 199 of NCERT
Exercise 10.3 – Page 200 of NCERT
Exercise 10.4 – Page 202 of NCERT
Exercise 10.5 – Page 203 of NCERT

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Exercise 10.1 Solution

Here you’ll find NCERT Chapter 10 – Practical Geometry Exercise 10.1 Solution.
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.

Answer:

The steps of construction are as follows.

Draw a line AB. Take a point P on it. Take a point C outside this line. Join C to P.
Taking P as centre and with a convenient radius, draw an arc intersecting line AB at point D and PC at point E.

Taking C as centre and with the same radius as before, draw an arc FG intersecting PC at H.
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.

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.

Answer:

The steps of construction are as follows.

Draw a line l and take a point P on line l. Then, draw a perpendicular at point P.
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.

Taking Y as centre and with a convenient radius, draw an arc intersecting l at A and XY at B.

Taking X as centre and with the same radius as before, draw an arc CD cutting XY at E.
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.

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?

Answer:

The steps of construction are as follows.

Draw a line l and take a point A on it. Take a point P not on l and join A to P.
Taking A as centre and with a convenient radius, draw an arc cutting l at B and AP at C.

Taking P as centre and with the same radius as before, draw an arc DE to intersect AP at F.
Adjust the compasses up to the length of BC. Without changing the opening of compasses and taking F as the centre, draw an arc to intersect the previously drawn arc DE at point G.

Join P to G to draw a line m. Line m will be parallel to line l.

Join P to any point Q on line l. Choose another point R on line m. Similarly, a line can be drawn through point R and parallel to PQ.

Let it meet line l at point S.

In quadrilateral PQSR, opposite lines are parallel to each other. PQ || RS and PR || QS
Thus, the quadrilateral PQSR is a parallelogram.

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Exercise 10.2 Solution

Here you’ll find NCERT Chapter 10 – Practical Geometry Exercise 10.2 Solution.
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.

Answer:

The rough figure of this triangle is as follows.

The required triangle is constructed as follows.

Draw a line segment YZ of length 5 cm.
Point X is at a distance of 4.5 cm from point Y. Therefore, taking point Y as centre, draw an arc of 4.5 cm radius.

Point X is at a distance of 6 cm from point Z. Therefore, taking point Z as centre, draw an arc of 6 cm radius. Mark the point of intersection of the arcs as X. Join XY and XZ.

XYZ is the required triangle.

Q2: Construct an equilateral triangle of side 5.5 cm.
Answer:

An equilateral triangle of side 5.5 cm has to be constructed. We know that all sides of an equilateral triangle are of equal length. Therefore, a triangle ABC has to be constructed with AB = BC = CA = 5.5 cm.

The steps of construction are as follows.

Draw a line segment BC of length 5.5 cm.
Taking point B as centre, draw an arc of 5.5 cm radius.

Taking point C as centre, draw an arc of 5.5 cm radius to meet the previous arc at point A.

Join A to B and C.

ABC is the required equilateral triangle.

Q3: Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

Answer:

The steps of construction are as follows.

(i) Draw a line segment QR of length 3.5 cm.

( ii) Taking point Q as centre, draw an arc of 4 cm radius.

Taking point R as centre, draw an arc of 4 cm radius to intersect the previous arc at point P.

Join P to Q and R.

ΔPQR is the required triangle. As the two sides of this triangle are of the same length (PQ = PR), therefore, ΔPQR is an isosceles triangle.

Q4: Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

Answer:

The steps of construction are as follows.

Draw a line segment BC of length 6 cm.
Taking point C as centre, draw an arc of 6.5 cm radius.

Taking point B as centre, draw an arc of radius 2.5 cm to meet the previous arc at point A.

((iv) Join A to B and C.

ΔABC is the required triangle. ∠B can be measured with the help of a protractor. It comes to 90º.

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Exercise 10.3 Solution

Here you’ll find NCERT Chapter 10 – Practical Geometry Exercise 10.3 Solution.
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°.

Answer:

The rough sketch of the required ΔDEF is as follows.

The steps of construction are as follows. (i)Draw a line segment DE of length 5 cm.

At point D, draw a ray DX making an angle of 90° with DE.
Taking D as centre, draw an arc of 3 cm radius. It will intersect DX at point F.

Join F to E. ΔDEF is the required triangle.

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°.

Answer: An isosceles triangle PQR has to be constructed with PQ = QR = 6.5 cm. A rough sketch of the required triangle can be drawn as follows.

The steps of construction are as follows.

Draw the line segment QR of length 6.5 cm.
At point Q, draw a ray QX making an angle 110° with QR.

Taking Q as centre, draw an arc of 6.5 cm radius. It intersects QX at point P.

Join P to R to obtain the required triangle PQR.

Q3: Construct ΔABC with BC = 7.5 cm, AC = 5 cm and m C = 60°.

Answer:

A rough sketch of the required triangle is as follows.

The steps of construction are as follows.

Draw a line segment BC of length 7.5 cm.
At point C, draw a ray CX making 60º with BC.

(iii) Taking C as centre, draw an arc of 5 cm radius. It intersects CX at point A.

(iv) Join A to B to obtain triangle ABC.

NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry Exercise 10.4 Solution

Here you’ll find NCERT Chapter 10 – Practical Geometry Exercise 10.4 Solution.
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.

Answer:

A rough sketch of the required ΔABC is as follows.

The steps of construction are as follows.
1. Draw a line segment AB of length 5.8 cm.

At point A, draw a ray AX making 60º angle with AB.
At point B, draw a ray BY, making 30º angle with AB.

Point C has to lie on both the rays, AX and BY. Therefore, C is the

(This is the required triangle ABC. point of intersection of these two rays.)

Q2: Construct ΔPQR if PQ = 5 cm, m PQR = 105° and m QRP = 40°. (Hint: Recall angle sum property of a triangle).

Answer:

A rough sketch of the required ΔPQR is as follows.

In order to construct ΔPQR, the measure of RPQ has to be calculated. According to the angle sum property of triangles,

∠PQR + ∠PRQ + ∠RPQ = 180º

105º + 40º + ∠RPQ = 180º

145º + ∠RPQ = 180º

RPQ = 180° – 145° = 35°

The steps of construction are as follows.

Draw a line segment PQ of length 5 cm.
At P, draw a ray PX making an angle of 35º with PQ.

At point Q, draw a ray QY making an angle of 105º with PQ.
Point R has to lie on both the rays, PX and QY. Therefore, R is the point of intersection of these two rays.

This is the required triangle PQR.

Q3: Examine whether you can construct ΔDEF such that EF = 7.2 cm, m E = 110° and m F = 80°. Justify your answer.

Answer:

Given that,

m∠E = 110° and m∠F = 80°
Therefore,

m∠E + m∠F = 110° + 80° = 190°

However, according to the angle sum property of triangles, we should obtain
m∠E + m∠F + m∠D = 180°.

Therefore, the angle sum property is not followed by the given triangle. And thus, we cannot construct ΔDEF with the given measurements.

Also, it can be observed that point D should lie on both rays, EX and FY, for constructing the required triangle. However, both rays are not intersecting each other. Therefore, the required triangle cannot be formed.