# NCERT Solutions for Class 7 Maths Chapter 6

## The Triangle and its Properties Class 7

### Exercise 6.1 : Solutions of Questions on Page Number : 116

Q1 :

In ΔPQR, D is the mid-point of .

is __________.

PD is __________.

Is QM = MR?

Answer :

(i) Altitude

(ii) Median

(iii) No

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Q2 :

Draw rough sketches for the following:

(a) In ΔABC, BE is a median.

(b) In ΔPQR, PQ and PR are altitudes of the triangle.

(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.

Answer :

(a)

(b)

(c)

Here, it can be observed that for ΔXYZ, YL is an altitude drawn exterior to side XZ which is extended up to point L.

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Q3 :

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Answer :

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### Exercise 6.2 : Solutions of Questions on Page Number : 118

Q1 :

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

Answer :

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Q2 :

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

Answer :

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### Exercise 6.3 : Solutions of Questions on Page Number : 121

Q1 :

Find the value of the unknown x in the following diagrams:

Answer :

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Q2 :

Find the value of the unknowns x and y in the following diagrams:

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### Exercise 6.4 : Solutions of Questions on Page Number : 126

Q1 :

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

Answer :

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Q2 :

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

(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

Answer :

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Q3 :

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

Answer :

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Q4 :

ABCD is quadrilateral.

Is AB + BC + CD + DA >AC + BD?

Answer :

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Q5 :

ABCD is quadrilateral.

Is AB + BC + CD + DA < 2 (AC + BD)?

Answer :

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Q6 :

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

Answer :

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### Exercise 6.5 : Solutions of Questions on Page Number : 130

Q1 :

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

Answer :

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Q2 :

ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.

Answer :

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Q3 :

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.

Answer :

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Q4 :

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

In the case of right-angled triangles, identify the right angles.

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Q5 :

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.

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Q6 :

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ2 + QR2= RP2

(ii) PQ2 + RP2= QR2

(iii) RP2 + QR2= PQ2

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Q7 :

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

Answer :

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Q8 :

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

Answer :

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Maths : CBSE NCERT Exercise Solutions for Class 7th for The Triangle and its Properties ( Exercise 6.1, 6.2, 6.3, 6.4, 6.5 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

 Exercise 6.1 Question 1 Question 2 Question 3
 Exercise 6.2 Question 1 Question 2
 Exercise 6.3 Question 1 Question 2
 Exercise 6.4 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6
 Exercise 6.5 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8