NCERT Solutions for Class 7 Maths Chapter 6

The Triangle and its Properties Class 7

Chapter 6 The Triangle and its Properties Exercise 6.1, 6.2, 6.3, 6.4, 6.5 Solutions

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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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<< Previous Chapter 5 : Lines and Angles Next Chapter 7 : Congruence of Triangles >>

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:


Answer :

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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.)


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Q4 :  

ABCD is quadrilateral.

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


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Q5 :  

ABCD is quadrilateral.

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


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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.


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Q2 :  

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


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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.


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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.


Answer :

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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.


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Q8 :  

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


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<< Previous Chapter 5 : Lines and Angles Next Chapter 7 : Congruence of Triangles >>

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.