Q.1 In

(i)

(ii)

(iii) Is QM = MR?

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i)

(ii)

(iii) No, QM

Q.2 Draw rough sketches for the following:

(a) In

(ib) In

(c) In

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Draw a Line segment AD

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i)

(ii)

(iii)

(iv)

(v)

(vi)

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i)

(ii)

(iii)

(iv)

(v)

(vi)

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i) we know that sum of all angle of a triangle = 180

Or,

(ii) we know that sum of all angle of a triangle = 180

Or,

Or,

(iii) we know that sum of all angle of a triangle = 180

Or,

(iv ) we know that sum of all angle of a triangle = 180

Or, 2x + 50° = 180°

Or, 2x = 180° – 50°

Or, 2x = 130°

(v) we know that sum of all angle of a triangle = 180

Or, 3

(vi) we know that sum of all angle of a triangle = 180

x + 2 x + 90° = 180° (

Or, 3x + 90° = 180°

Or, 3x = 180° – 90°

Or, 3x = 90°

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i)

70° +

Thus

(ii)

Thus,

(iii)

Or,

Thus,

(iv)

Or,

Or,

Thus,

(v)

Or, 2

Or, 2

Or, 2

Thus,

(vi) From the given figure, we have

Adding both sides, we have
Adding both sides, we have
Adding both sides, we have

Or, 180° = 3

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

(i) 2 cm, 3 cm, 5 cm

(ii) 3 cm, 6 cm, 7 cm

(iii) 6 cm, 3 cm, 2 cm

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

We know that for a triangle, the sum of any two sides must be greater than the third side.

(i) Given sides are 2 cm, 3 cm, 5 cm

(2 + 3) = 5

5 = 5

Hence, the triangle is not possible.

(i) Given sides are 3 cm, 6 cm, 7 cm

(3 + 6) = 9 > 7

(6 + 7) = 13 > 3

(7 + 3) = 10 > 6

Hence, the triangle is possible.

(iii) Given sides are 6 cm, 3 cm, 2 cm

(3 + 2) = 5 < 6

Hence, the triangle is not possible.

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

(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i) Yes,

So, OP + OQ > PQ

(ii) Yes,

So, OQ + OR > QR

(iii) Yes,

So, OR + OP > RP

Q.3 AM is a median of a

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

We know that,

The sum of the length of any two sides is always greater than the third side.

Now In

Here, AB + BM > AM … [equation i]

Then, In

Here, AC + CM > AM … [equation ii]

By adding equation [i] and [ii] we get,

AB + BM + AC + CM > AM + AM

From the figure we have, BC = BM + CM

AB + BC + AC > 2 AM

Hence, the given expression is true.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

In

AB + BC > AC …(i)
[Sum of any two sides is greater than the third side]

In

BC + CD > BD …(ii)

In

In

Adding eq. (i), (ii), (iii) and (iv), we get

2AB + 2BC + 2CD + 2DA > 2AC + 2BD

Or, AB + BC + CD + DA > AC + BD [Dividing both sides by 2]

Hence, proved

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

In

BC < BO + CO …(ii)

In

CD < CO + DO …(iii)

In

DA < DO + AO …(iv)

Adding eq. (i), (ii), (iii) and (iv), we have

AB + BC + CD + DA < 2AO + 2BO + 2CO + 2DO

Or, AB + BC + CD + DA < 2(AO + BO + CO + DO)

Or, AB + BC + CD + DA < 2 [(AO + CO) + (BO + DO)]

Or, AB + BC + CD + DA < 2(AC + BD)

Thus, AB + BC + CD + DA < 2(AC + BD)

Hence, proved.

Q.6 The length of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Sum of two sides

= 12 cm + 15 cm = 27 cm

Difference of the two sides

= 15 cm – 12 cm = 3 cm

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

In right angled triangle PQR, we have

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

In right angled?ABC, we have

Or,

Or,

Or,

Thus, the required length of BC = 24 cm.

Q.3 A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Here, the ladder forms a right angled triangle.

Or,

Or,

Or,

Thus, the distance of the foot from the ladder = 9m

Q.4 Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm.

(ii) 2 cm, 2 cm, 5 cm.

(iii) 1.5 cm, 2 cm, 2.5 cm

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

(i) Given sides are 2.5 cm, 6.5 cm, 6 cm.

Square of the longer side =

Sum of the square of other two sides
=

Since, the square of the longer side in a triangle is equal to the sum of the squares of other two sides.

(ii) Given sides are 2 cm, 2 cm, 5 cm .

Square of the longer side =

Sum of the square of other two sides
=

(iii) Given sides are 1.5 cm, 2 cm, 2.5 cm

Square of the longer side =

Sum of the square of other two sides
=

Since the square of longer side in a triangle is equal to the sum of square of other two sides.

Q.5 A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree . Find the original height of the tree.

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Let AB be the original height of the tree and broken at C touching the ground at D such that

AC = 5 m

and AD = 12 m

In right triangle

Or,

Or, 144 + 25 =

But CD = BC

AC + CB = AB

5 m + 13 m = AB

Thus, the original height of the tree = 18 m.

Q.6 Angles Q and R of a APQR are 25° and 65°. Write which of the following is true.

(i)

(ii)

(iii)

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

We know that

(i) Not True

(ii) True

(iii) Not True

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Length of rectangle = 40cm

Diagonal = 41 cm

Or,

Or, breath =

Breath = 9 cm

Perimeter of rectangle = 2×(40+9) = 2×49 = 98 cm

NCERT Solutions for Class 7 Maths Chapter 6 The Triangle And Its Properties

Answer :

Let ABCD be a rhombus whose diagonals intersect each other at O such that AC = 16 cm and BD = 30 cm

Since, the diagonals of a rhombus bisect each other at 90°.

In right

=

Since AB = BC = CD = DA (Property of rhombus)

There are total 21 questions present in ncert solutions for class 7 maths chapter 6 the triangle and its properties

There are total 3 long question/answers in ncert solutions for class 7 maths chapter 6 the triangle and its properties

There are total 5 exercise present in ncert solutions for class 7 maths chapter 6 the triangle and its properties