CBSE Class 7

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4 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 6.4.

• The Triangle and its Properties Class 7 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 6.5
• The Triangle and its Properties Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4

Question 1.
Is it possible to have a triangle with the following sides?

1. 2 cm, 3 cm, 5 cm
2. 3 cm, 6 cm, 7 cm
3. 6 cm, 3 cm, 2 cm.

Solution:

1. Since, 2 + 3 > 5
   So the given side lengths cannot form a triangle.
2. We have, 3 + 6 > 7, 3 + 7 > 6 and 6 + 7 > 3
   i. e., the sum of any two sides is greater than the third side.
   So, these side lengths form a triangle.
3. We have, 6 + 3 > 2, 3 + 2 \(\ngtr \) 6
   So, the given side lengths cannot form a triangle.

Question 2.
Take any point O in the interior of a triangle PQR. Is

1. OP + OQ > PQ ?
2. OQ + OR > QR?
3. OR + OP > RP ?

Solution:

1. Yes ! OP + OQ > PQ …(1)
   Sum of the lengths of any two sides of a triangle is greater than the length of the third side
2. Yes! OQ + OR > QR …(2)
   Sum of the lengths of any two sides of a triangle is greater than the length of the third side
3. Yes! OR + OP > RP …(3)
   Sum of the lengths of any two sides of a triangle is greater than the length of the third side

Question 3.
AM is a median of a triangle ABC. Is AB + BC + CA > 2 AM?
(Consider the sides of triangles ∆ ABM and ∆ AMC.)

Solution:
Using triangle inequality property in triangles ABM and AMC, we have
AB + BM > AM …(1) and, AC + MC > AM …(2)
Adding (1) and (2) on both sides, we get
AB + (BM + MC) + AC > AM + AM
⇒ AB + BC + AC > 2AM

Question 4.
ABCD is a quadrilateral.
Is AB + BC + CD + DA > AC + BD ?

Solution:
In ∆ ABC, AB + BC > AC …(1)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
In ∆ ACD, CD + DA > AC …(2)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
Adding (1) and (2),
AB + BC + CD + DA > 2AC …(3)
In ∆ ABD, AB + DA > BD …(4)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
In ∆ BCD, BC + CD > BD …(5)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
Adding (4) and (5),
AB + BC + CD + DA > 2BD …(6)
Adding (3) and (6),
2 [AB + BC + CD + DA] > 2 (AC + BD)
⇒ AB + BC + CD + DA > AC + BD.

Question 5.
ABCD is a quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?

Solution:
In ∆ OAB, OA + OB > AB ….(1)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side.
In ∆ OBC, OB + OC > BC ….(2)
Sum of the lengths of any two sides of a triangle la greater than the length of the third side.
In ∆ OCA,OC + OA > CA ….(3)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
In ∆ OAD, OA + OD > AD ….(4)
Sum of the lengths of any two sides of a triangle is greater than the length of the third side
Adding (1), (2), (3) and (4),
2(OA + OB + OC + OD) > AB + BC + CD + DA
⇒ AB + BC + CD + DA < 2 (OA + OB + OC + OD)
⇒ AB + BC + CD + DA < 2(OA + OC + OB + OD)
⇒ AB + BC + CD + DA < 2 (AC + BD).

Question 6.
The lengths of the two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
Solution:
Let x cm be the length of the third side.
∴ Sum of the lengths of any two sides of a triangle is greater than the length of the third side.
∴ We should have

∴ The length of the third side should be any length between 3 cm and 27 cm.

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and it’s Properties Ex 6.4 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.4, 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 6.3 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 6.3.

• The Triangle and its Properties Class 7 Ex 6.1
• The Triangle and its Properties Class 7 Ex 6.2
• 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

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3

Question 1.
Find the value of the unknown x in the following diagrams:

Solution:

Question 2.
Find the values of the unknowns x and y in the following diagrams:

Solution:

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3, 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 6.2 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 6.2.

• The Triangle and its Properties Class 7 Ex 6.1
• 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

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.2

Question 1.
Find the value of the unknown exterior angle x in the following diagrams:

Solution:

Question 2.
Find the value of the unknown interior angle x in the following figures:

Solution:

We hope the NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.2 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2.

• Lines and Angles Class  7 Ex 5.1
• Lines and Angles Class  7 MCQ

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

Question 1.
State the property that is used in each of the following statements?

1. If a || b, then ∠ 1 = ∠ 5.
2. If ∠ 4 = ∠ 6, then a || b.
3. If ∠ 4 + ∠ 5 = 180°, then a || b.

Solution:

1. Corresponding angle property.
2. Alternate interior angle property.
3. Interior angles on the same side of the transversal are supplementary.

Question 2.
In the following figure, identify:

1. the pairs of corresponding angles.
2. the pairs of alternate interior angles.
3. the pairs of interior angles on the same side of the transversal.
4. the vertically opposite angles.

Solution:

1. ∠1, ∠5; ∠2, ∠6; ∠3, ∠7 and ∠4, ∠8 are four pairs of corresponding angles.
2. ∠2, ∠8, and ∠3, ∠5 are two pairs of alternate interior angles.
3. ∠2, ∠5, and ∠3, ∠8 are two pairs of interior angles on the same side of the transversal.
4. ∠1, ∠3; ∠2, ∠4; ∠5, ∠7 and ∠6, ∠8 are four pairs of vertically opposite angles.

Question 3.
In the adjoining figure, p || q. Find the unknown angles.
Solution:
a = 55°, b = 125°, c = 55°, d = 125°, e = 55°, f = 55°.

Question 4.
Find the value of x in each of the following figures if l || m.

Solution:
(i) Since, l || m and t is a transversal.
∴ ∠x = (180° – 110°) = 70° [Corresponding angles, Linear pair]

(ii) if l || m and a is a transversal.
Then, ∠x = 1000 [Corresponding angles]

Question 5.
In the given figure, the arms of two angles are parallel. If ∠ ABC = 70°, then find

Solution:

1. 70°
2. 70°

Question 6.
In the given figures below, decide whether l is parallel to m.


Solution:

1. l is not parallel to m
2. l is not parallel to m
3. l || m
4. l is not parallel to m

We hope the NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4.

• Simple Equations Class 7 Ex 4.1
• Simple Equations Class 7 Ex 4.2
• Simple Equations Class 7 Ex 4.3
• Simple Equations Class 7 MCQ

NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4

Question 1.
Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add 4 to eight times a number; you get 60.
(b) One-fifth of a number minus 4 gives 3.
(c) If I take three-fourths of a number and add 3 to it, I get 21.
(d) I subtracted 11 from twice a number, the result was 15.
(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
(g) Anwar thinks of a number. If he takes away 7 from \(\frac { 5 }{ 2 } \) of the number, the result is 23.

Solution:

Question 2.
Solve the following:
(a) The teacher tells the class that the highest marks obtained by a student in her class are twice the lowest mark plus 7. The highest score is 87. What is the lowest score?
(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).
(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?
Solution:

Question 3.
Solve the following:

1. Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?
2. Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?
3. The people of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees was two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was 77?

Solution:

Question 4.
Solve the following riddle :
I am a number, Tell me my identity!
Take me seven times over And add a fifty!
To reach a triple century You still need forty!
Solution:
Let ‘x’ be the number,
Then, according to the question, we get (x × 7) + 50 = 300 – 40
7x + 50 = 260
7x = 210
x = \(\frac { 210 }{ 7 } \) = 30
So, the number is 30.

We hope the NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4 help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.4, drop a comment below and we will get back to you at the earliest.