NCERT Solutions for Class 7 Maths

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1.

• Practical Geometry Class 7 Ex 10.2
• Practical Geometry Class 7 Ex 10.3
• Practical Geometry Class 7 Ex 10.4
• Practical Geometry Class 7 Ex 10.5

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 10
Chapter Name	Practical Geometry
Exercise	Ex 10.1
Number of Questions Solved	3
Category	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1

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

1. Draw a line AB.
2. Take a point C outside it.
3. Take any point D on AB.
4. Join C to D.
   
5. with D as centre and a convenient radius, draw an arc cutting AB at F and CD at E.
6. Now with C as centre and the same radius as in step 5, draw an arc GH cutting CD at I.
7. Place the pointed tip of the compasses at F and adjust the opening so that the pencil tip is at E.
8. With the same opening as in step 7 and with I as centre, draw an arc cutting the arc GH at J.
9. Now join CJ to draw a line ‘KL’. Then KL is the required line.

Question 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 of Construction

1. Draw a line l.
2. Take any point A on line l.
   
3. Construct an angle of 90° at point A of line l and draw a line AL perpendicular to line l.
4. Mark a point X on AL such that AX = 4 cm.
5. At X construct an angle of 90° and draw a line XC perpendicular to line AL.
6. Then line XC (line m) is the required line through X such that m || l.

Question 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 of Construction

1. Draw a line l and take a point P not on it.
2. Take any point Q on l.
3. Join Q to P.
   
4. Draw a line m parallel to line l, as shown in the figure. Then line m || line l.
5. Join P to any point Q on l.
6. Choose any point R on m.
7. Join R to Q.
8. Through R, draw a line n parallel to the line PQ.
9. Let the line n meet the line l at S.
10. Then, the shape enclosed by the two sets of parallel lines is a parallelogram.

We hope the NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.1 helps you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry EX 10.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1.

• Rational Numbers Class 7 Ex 9.2
• Rational Numbers Class 7 MCQ

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 9
Chapter Name	Rational Numbers
Exercise	Ex 9.1
Number of Questions Solved	10
Category	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

Question 1.
List five rational numbers between

1. -1 and 0
2. -2 and -1
3. –\(\frac { 4 }{ 5 } \) and – \(\frac { 2 }{ 3 } \)
4. –\(\frac { 1 }{ 2 } \) and \(\frac { 2 }{ 3 } \)

Solution:

Question 2.
Write four more rational numbers in each of the following patterns :

Solution:

Question 3.
Give four rational numbers equivalent to:
(i) \(\frac { -2 }{ 7 } \)
(ii) \(\frac { 5 }{ -3 } \)
(iii) \(\frac { 4 }{ 9 } \)

Solution:
(i) Four rational numbers equivalent to \(\frac { -2 }{ 7 } \) are

(ii) Four rational numbers equivalent to \(\frac { 5 }{ -3 } \) are

(iii) Four rational numbers equivalent to \(\frac { 4 }{ 9 } \) are

Question 4.
Draw the number line and represent the following rational numbers on it:

1. \(\frac { 3 }{ 4 } \)
2. \(\frac { -5 }{ 8 } \)
3. \(\frac { -7 }{ 4 } \)
4. \(\frac { 7 }{ 8 } \)

Solution:

Question 5.
The points P, Q, R, S, T, U, A, and B on this number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S.

Solution:
The rational number represented by P is 2 \(\frac { 1 }{ 3 } \) = \(\frac { 7 }{ 3 } \)
The rational number represented by Q is 2 \(\frac { 2 }{ 3 } \) = \(\frac { 8 }{ 3 } \)
The rational number represented by R is -1 \(\frac { 1 }{ 3 } \) = \(\frac { -4 }{ 3 } \)
The rational number represented by S is -1 \(\frac { 2 }{ 3 } \) = \(\frac { -5 }{ 3 } \)
The rational numbers represented by P, Q, R and S are 2 \(\frac { 1 }{ 3 } \), 2 \(\frac { 2 }{ 3 } \), -1 \(\frac { 1 }{ 3 } \) and – 1 \(\frac { 2 }{ 3 } \) respectively

Question 6.
Which of the following pairs represent the same rational number?

Solution:
(i) \(\frac { -7 }{ 21 } \) is a negative rational number and \(\frac { 3 }{ 9 } \) is a positive rational number. So, the given pair does not represent the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.
(vi) \(\frac { 1 }{ 3 } \) is a positive rational number and \(\frac { -1 }{ 9 } \) is a negative rational number. So, the given pair does not present the same rational number.

Thus, \(\frac { -5 }{ -9 } \) is a positive rational number and \(\frac { 5 }{ -9 } \) is a negative rational number. So, the given pair does not represent the same rational number.

Question 7.
Rewrite the following rational numbers in the simplest form :

Solution:

Question 8.
Fill in the boxes with the correct symbol out of >, < and =

Solution:

Question 9.
Which is greater in each of the following?


Solution:

Question 10.
Write the following rational numbers in ascending order :

Solution:

We hope the NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1.

• Comparing Quantities Class 7 Ex 8.2
• Comparing Quantities Class 7 Ex 8.3
• Comparing Quantities Class 7 MCQ

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 8
Chapter Name	Comparing Quantities
Exercise	Ex 8.1
Number of Questions Solved	3
Category	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1

Question 1.
Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hour

Solution:
(a) ₹ 5 : 50 paise
= ₹ 5 : 50 paise
= 5 × 100 paise : 50 paise
= 500 paise : 50 paise
= 10 : 1.

(b) 15 kg to 210g
= 15 kg : 210g
= 15 × 1000 g : 210g
= 15000 g : 210g = 500:7.

(c) 9 m to 27 cm
= 9m : 27 cm = 9 × 100 cm : 27 cm
= 900 cm : 27 cm
900 : 27 = 100 : 3.

(d) 30 days to 36 hours
= 30 days : 36 hours
30 × 24 hours : 36 hours
= 720 hours : 36 hours
= 720 : 36 = 20 : 1.

Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:
Let x computers be needed for 24 students.

Hence, 12 computers will be needed for
24 students.
Aliter:
In a computer lab,
Every 6 students need 3 computers.
∴ Every 1 student needs \(\frac { 3 }{ 6 } \) computers.
∴ Every 24 students need \(\frac { 3 }{ 6 } \) × 24 = 3 × 4 = 12 computers

Question 3.
Population of Rajasthan = 570 lakhs
and population of UP = 1660 lakhs.
Area of Rajasthan =3 lakh km2
and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?
Solution:
(i) Number of people per sq. km. in Rajasthan state

(ii) The Rajasthan State is less populated.

We hope the NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1 helps you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1.

• Congruence of Triangles Class 7 Ex 7.2
• Congruence of Triangles Class 7 MCQ

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 7
Chapter Name	Congruence of Triangles
Exercise	Ex 7.1
Number of Questions Solved	4
Category	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1

Question 1.
Complete the following statements:
(a) Two line segments are congruent if……..
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is…….
(c) When we write ∠A = ∠B, we actually mean….
Solution:
(a) they have the same length
(b) 70°
(c) m∠A = m∠B

Question 2.
Give any two real-life examples for congruent shapes.
Solution:

1. Two coins or notes of the same denomination.
2. Two keys of the same lock.

Question 3.
If ∆ ABC = ∆ FED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Solution:
Corresponding vertices: A and F; B and E; C and D.
Corresponding sides : \(\overline { AB } \) and \(\overline { FE } \) ; \(\overline { BC } \) and \(\overline { ED } \); \(\overline { CA } \) and \(\overline { DF } \).
Corresponding angles: ∠A and ∠F; ∠B and ∠E; ∠C and ∠D.

Question 4.
If ∆ DEF = ∆ BCA, write the part(s) of ∆ BCA that correspond to

1. ∠E
2. \(\overline { EF } \)
3. ∠F
4. \(\overline { DF } \)

Solution:

1. ∠C
2. \(\overline { CA } \)
3. ∠A
4. \(\overline { BA } \)

We hope the NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1.

• The Triangle and its Properties Class 7 Ex 6.2
• The Triangle and its Properties Class 7 Ex 6.3
• The Triangle and its Properties Class 7 Ex 6.4
• The Triangle and its Properties Class 7 Ex 6.5
• The Triangle and its Properties Class 7 MCQ

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 6
Chapter Name	The Triangle and its Properties
Exercise	Ex 6.1
Number of Questions Solved	3
Category	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1

Question 1.
In ∆PQR, D is the mid-point of \(\overline { QR } \).

Solution:
\(\overline { PM } \) is the altitude.
PD is the median.
No! QM ≠ MR.

Question 2.
Draw rough sketches for the following:

(a) In ∆ ABC, BE is a median.
(b) In ∆ PQR, PQ and PR are altitudes of the triangle.
(c) In ∆ XYZ, YL is an altitude in the exterior of the triangle.

Solution:

Question 3.
Verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same.
Solution:
AD is the median.
AL is the altitude.

Draw a line segment BC. By paper folding, locate the perpendicular bisector of BC. The folded crease meets BC at D, its mid-point.
Take any point A on this perpendicular bisector. Join AB and AC. The triangle thus obtained is an isosceles ∆ABC in which AB = AC.
Since D is the mid-point of BC, so AD is its median. Also, AD is the perpendicular bisector of BC. So, AD is the altitude of ∆ABC.
Thus, it is verified that the median and altitude of an isosceles triangle are the same.

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and it’s Properties Ex 6.1 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.1, drop a comment below and we will get back to you at the earliest.