NCERT Grade 7-The Triangle and its Properties-Questions

NCERT Solutions for Class 7 Maths

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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.

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