NCERT Grade 7-The Triangle and its Properties-Questions

NCERT Solutions for Class 7 Maths

Find 100% accurate solutions for NCERT Class VII Science. All questions have been explained and solved step-by-step, to help you understand thoroughly. Free Download option available!

Sign Up to Download as PDF

The Triangle and its Properties

Exercise 1

1.    In A PQR, D is the mid-point of 

 is ____

PD is _____

Is QM = MR ?

2.   Draw rough sketches for the following:

In A ABC, BE is a median.

In A PQR, PQ and PR are altitudes of the triangle.

In A XYZ, YL is an altitude in the exterior of the triangle.

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

Exercise 2

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


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

Exercise 3

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

7.    Find the values of the unknowns x and y in the following diagrams:

Exercise 4

8.    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

9.   Take any point 0 in the interior of a triangle PQR. Is:

(i) OP + OQ > PQ ?

(ii) OQ + OR > QR ?

(iii) OR + OP > RP ? Since sum of two sides is greater than third side.


10.  AM is a median of a triangle ABC. Is AB + BC + CA > 2AM?

(Consider the sides of triangles Δ ABM and Δ AMC.)

11.   ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

12.  ABCD is quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?

13.  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 5

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

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

16.  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.

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

(i) 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.


18.  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.

19.  Angles Q and R of a Δ PQR are 25° and 65°. Write which of the following is true:

(i) PQ2 + QR2 = RP2

(ii) PQ2 + RP2 = QR2

(iii) RP2 + QR2 = PQ2

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

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

MySchoolPage connects you with exceptional, certified math tutors who help you stay focused, understand concepts better and score well in exams!

Have a Question?




Mathematics - Videos


Physics - Videos


Biology - Videos


Chemistry - Videos