NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

*According to the latest CBSE Syllabus 2023-24, this chapter has been removed.

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry download the PDF are given below. The foremost objective is to help students understand and crack these problems. We at BYJUâ€™S, have prepared the NCERT Solutions for Class 7 Maths and solved them step-by-step with complete descriptions.

There are 5 exercises present in Chapter 10 â€“ Practical Geometry of NCERT Solutions for Class 7 Maths. The concepts covered in this chapter include

• Construction of a Line Parallel to a Given Line, through a Point Not on the Line
• Construction of Triangle
• Constructing a Triangle When the Lengths of Its Three Sides Are Known (SSS Criterion)
• Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle between Them Are Known (SAS Criterion)
• Constructing a Triangle When The Measures of Two of Its Angles and the Length of the Side Inclined between Them Is Given (ASA Criterion)
• Constructing a Right-Angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

Access Exercises of NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

Exercise 10.1 Solutions

Exercise 10.2 Solutions

Exercise 10.3 Solutions

Exercise 10.4 Solutions

Exercise 10.5 Solutions

Access Answers to NCERT Class 7 Maths Chapter 10 â€“ Practical Geometry

Exercise 10.1 Page: 196

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 for construction

1. Draw a line AB.

2. Take any point Q on AB and a point P outside AB and join PQ.

3. With Q as the centre and any radius, draw an arc to cut AB at E and PQ at F.

4. With P as the centre and the same radius, draw an arc IJ to cut QP at G.

5. Place the pointed tip of the compass at E and adjust the opening so that the pencil tip is at F.

6. With the same opening as in step 5 and with G as the centre, draw an arc cutting the arc IJ at H.

7. Now, join PH to draw a line CD.

2. 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.

Solution:-

Steps for construction

1. Draw a line L.

2. Take any point P on line L.

3. At point P, draw a perpendicular line N.

4. Place the pointed tip of the compass at P and adjust the compass up to length of 4 cm, draw an arc to cut this perpendicular at point X.

5. At point X, again draw a perpendicular line M.

3. 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?

Solution:-

Steps for construction

1. Draw a line L.

2. Take any point Q on L and a point P outside L and join PQ.

3. Make sure that angles at point P and point Q are equal, i.e., âˆ Q = âˆ P

4. At point P, extend the line to get line M which is parallel L.

5. Then take any point R on line M.

6. At point R, draw an angle such that âˆ P = âˆ R.

7. At point R, extend the line which intersects line L at S and draw a line RS.

Exercise 10.2 Page: 199

1. Construct Î”XYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

Solution:-

Steps of construction

1. Draw a line segment YZ = 5 cm.

2. With Z as a centre and radius 6 cm, draw an arc.

3. With Y as a centre and radius 4.5 cm, draw another arc, cutting the previous arc at X.

4. Join XY and XZ.

Then, Î”XYZ is the required triangle.

2. Construct an equilateral triangle of side 5.5 cm.

Solution:-

Steps of construction

1. Draw a line segment AB = 5.5 cm.

2. With A as a centre and radius 5.5 cm, draw an arc.

3. With B as a centre and radius 5.5 cm, draw another arc, cutting the previous arc at C.

4. Join CA and CB.

Then, Î”ABC is the required equilateral triangle.

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

Solution:-

Steps of construction

1. Draw a line segment QR = 3.5 cm.

2. With Q as a centre and radius 4 cm, draw an arc.

3. With R as a centre and radius 4 cm, draw another arc, cutting the previous arc at P.

4. Join PQ and PR.

Then, Î”PQR is the required isosceles triangle.

4. Construct Î”ABC, such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure âˆ B.

Solution:-

1. Draw a line segment BC = 6 cm.

2. With B as a centre and radius 2.5 cm, draw an arc.

3. With C as a centre and radius 6.5 cm, draw another arc, cutting the previous arc at A.

4. Join AB and AC.

Then, Î”ABC is the required triangle.

5. When we will measure the angle B of triangle by a protractor, the angle is equal to âˆ B = 90o

Exercise 10.3 Page: 200

1. Construct Î”DEF such that DE = 5 cm, DF = 3 cm and mâˆ EDF = 90o.

Solution:-

Steps of construction

1. Draw a line segment DF = 3 cm.

2. At point D, draw a ray DX to making an angle of 90o, i.e., âˆ XDF = 90o.

3. Along DX, set off DE = 5cm.

4. Join EF.

Then, Î”EDF is the required right-angled triangle.

2. Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110o.

Solution:-

Steps of construction

1. Draw a line segment AB = 6.5 cm.

2. At point A, draw a ray AX to making an angle of 110o, i.e., âˆ XAB = 110o.

3. Along AX, set off AC = 6.5cm.

4. Join CB.

Then, Î”ABC is the required isosceles triangle.

3. Construct Î”ABC with BC = 7.5 cm, AC = 5 cm and mâˆ C = 60Â°.

Solution:-

Steps of construction

1. Draw a line segment BC = 7.5 cm.

2. At point C, draw a ray CX to making an angle of 60o, i.e., âˆ XCB = 60o.

3. Along CX, set off AC = 5cm.

4. Join AB.

Then, Î”ABC is the required triangle.

Exercise 10.4 Page: 202

1. Construct Î”ABC, given m âˆ A =60o, m âˆ B = 30o and AB = 5.8 cm.

Solution:-

Steps of construction:

1. Draw a line segment AB = 5.8 cm.

2. At point A, draw a ray P to making an angle of 60o, i.e., âˆ PAB = 60o.

3. At point B, draw a ray Q to making an angle of 30o, i.e., âˆ QBA = 30o.

4. Now, the two rays â€“ AP and BQ â€“ intersect at point C.

Then, Î”ABC is the required triangle.

2. Construct Î”PQR if PQ = 5 cm, mâˆ PQR = 105o and mâˆ QRP = 40o.

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

Solution:-

We know that the sum of the angles of a triangle is 180o.

âˆ´ âˆ PQR + âˆ QRP + âˆ RPQ = 180o

= 105o+ 40o+ âˆ RPQ = 180o

= 145o + âˆ RPQ = 180o

= âˆ RPQ = 180oâ€“ 1450

= âˆ RPQ = 35o

Hence, the measures of âˆ RPQ is 35o.

Steps of construction

1. Draw a line segment PQ = 5 cm.

2. At point P, draw a ray L to making an angle of 105o, i.e., âˆ LPQ = 35o.

3. At point Q, draw a ray M to making an angle of 40o, i.e., âˆ MQP = 105o.

4. Now, the two rays â€“ PL and QM â€“ intersect at point R.

Then, Î”PQR is the required triangle.

3. Examine whether you can construct Î”DEF, such that EF = 7.2 cm, mâˆ E = 110Â° and mâˆ F = 80Â°. Justify your answer.

Solution:-

From the question, it is given that

EF = 7.2 cm

âˆ E = 110o

âˆ F = 80o

Now, we have to check whether it is possible to construct Î”DEF from the given values.

We know that the sum of the angles of a triangle is 180o.

Then,

âˆ D + âˆ E + âˆ F = 180o

âˆ D + 110o+ 80o= 180o

âˆ D + 190o = 180o

âˆ D = 180oâ€“ 1900

âˆ D = -10o

We may observe that the sum of two angles is 190o is greater than 180o. So, it is not possible to construct a triangle.

Exercise 10.5 Page: 203

1. Construct the right-angled Î”PQR, where mâˆ Q = 90Â°, QR = 8cm and PR = 10 cm.

Solution:-

Steps of construction

1. Draw a line segment QR = 8 cm.

2. At point Q, draw a ray QY to making an angle of 90o, i.e., âˆ YQR = 90o.

3. With R as a centre and radius 10 cm, draw an arc that cuts the ray QY at P.

4. Join PR.

Then, Î”PQR is the required right-angled triangle.

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

Solution:-

Let us consider Î”ABC is a right-angled triangle at âˆ B = 90o

Then,

AC is hypotenuse = 6 cm â€¦ [Given in the question]

BC = 4 cm

Now, we have to construct the right-angled triangle by using the above values.

Steps of construction

1. Draw a line segment BC = 4 cm.

2. At point B, draw a ray BX to making an angle of 90o, i.e., âˆ XBC = 90o.

3. With C as a centre and radius 6 cm, draw an arc that cuts the ray BX at A.

4. Join AC.

Then, Î”ABC is the required right-angled triangle.

3. Construct an isosceles right-angled triangle ABC, where mâˆ ACB = 90Â° and AC = 6 cm.

Solution:-

Steps of construction

1. Draw a line segment BC = 6 cm.

2. At point C, draw a ray CX to making an angle of 90o, i.e., âˆ XCB = 90o.

3. With C as a centre and radius 6 cm, draw an arc that cuts the ray CX at A.

4. Join AB.

Then, Î”ABC is the required right-angled triangle.

Disclaimer:

Dropped Topics- 10.1 Introduction, 10.2 Construction of a line parallel to a given line, through a point not on the line, 10.3 Construction of triangles, 10.4 Constructing a triangle when lengths of its three sides are known (SSS criterion), 10.5 Constructing a triangle when the lengths of two sides and the measure of the angle between them are known (SAS criterion), 10.6 Constructing a triangle when the measures of two of its angles and the length of the side included between them is given (ASA criterion),
10.7 Constructing a right-angled triangle when the length of one leg and its hypotenuse are given (RHS criterion).

Frequently Asked Questions on NCERT Solutions for Class 7 Maths Chapter 10

Q1

What is the importance of studying NCERT Solutions for Class 7 Maths Chapter 10?

The solutions of NCERT Class 7 Maths Chapter 10 help students in understanding the summary of the question paper pattern, including a variety of questions, repeated questions, concise and long answer type questions, multiple-choice questions, marks, etc. The more types of questions students solve, the more marks they score.
Q2

Mention concepts that are important from an exam perspective in NCERT Solutions for Class 7 Maths Chapter 10.

The important concepts from an exam perspective in NCERT Solutions for Class 7 Maths Chapter 10 are construction of a line parallel to a given line, through a point not on the line,Â construction of triangle, constructing a triangle when the lengths of its three sides are known (SSS Criterion), constructing a triangle when the lengths of two sides and the measure of the angle between them are known (SAS Criterion), constructing a triangle when the measures of two of Its angles and the length of the side inclined between them is given (ASA Criterion) and constructing a right-angled triangle when the length of one leg and its hypotenuse are given (RHS Criterion).
Q3

How many exercises are there in NCERT Solutions for Class 7 Maths Chapter 10?

There are 5 exercises in NCERT Solutions for Class 7 Maths Chapter 10. The first exercise has 3 questions, the second exercise has 4 questions, the third exercise has 2 questions with many sub-questions, the fourth exercise has 3 questions and the last and final exercise has 3 questions, based on constructing a right-angled triangle when the length of one leg and its hypotenuse are given (RHS criterion).