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
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
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.
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 :
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)