# 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?

(i) Altitude

(ii) Median

(iii) No

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.

(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.

Q3 :

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

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

Q1 :

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

Q2 :

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

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

Q1 :

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

Q2 :

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

### 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

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?

Q3 :

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

Q4 :

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

Q5 :

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

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?

### 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.

Q2 :

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

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.

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.

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.

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

Q7 :

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

Q8 :

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