Class 7 Maths The Triangle And Its Properties | Important Questions For Practice

IMPORTANT QUESTIONS FOR CBSE EXAMINATION | CLASS 7 MATHEMATICS
THE TRIANGLE AND ITS PROPERTIES

Answer the following (2 marks):

1. An exterior angle of a triangle is of measure 70 degree and one of its interior opposite angles is of measure 25 degree. Find the measure of the other interior opposite angle?

2. The two interior opposite angles of an exterior angle of a triangle are 60 degree and 80 degree. Find the measure of the exterior angle?

3. Two angles of a triangle are 30 degree and 80 degree. Find the third angle?

4. One of the angles of a triangle is 80 degree and the other two angles are equal. Find the measure of each of the equal angles?

5. The three angles of a triangle are in the ratio 1: 2: 1. Find all the angles of the triangle.

6. Is it possible to have a triangle with the following sides?
a) 3 cm, 4 cm, 5 cm
b) 2 cm, 3 cm, 6 cm

7. The lengths of two sides of a triangle are 12 cm and 16 cm. Between which two numbers can length of the third side fall?

8. ABC is a triangle, right angled at A. If AB = 8 cm, AC = 6 cm, find BC?

9. Find the perimeter of a rectangle whose length is 20 cm and a diagonal is 25 cm.

10. The diagonals of a rhombus measure 8 cm and 6 cm, find its perimeter?

ANSWERS:

1. An exterior angle of a triangle is equal to the sum of its interior opposite angles. Given exterior angle = 70 degree and one interior angle = 25 degree.
Other angle = 70 -25 = 45

2. Measure of an exterior angle = 60 + 80 = 140

3. The total measure of the three angles of a triangle is 180 degree.
Third angle = 180 – (30 + 80)
= 180 – 110 = 70

4. Let the angle be x.
By angle sum property, 80 + x + x = 180
80 + 2x = 180
2x = 180 – 80 = 100
x = 100/2 = 50

5. Sum of the parts =1+2+1=4
First angle = 180 x 1/4 =45
Second angle = 180 x 2/4 = 360/4 = 90
Third angle = 180 x ¼ = 45

6. Suppose such a triangle is possible. Then the sum of the lengths of any two sides would be greater than the length of the third side.
a) 3 + 4 >5
4 + 5>3
3 + 5 > 4
Therefore, the triangle is possible.
b) 2 + 3 < 6
3 + 6 > 2
2 + 6 > 3
Therefore, the triangle is not possible.

7. We know that the sum of two sides of a triangle is always greater than the third.
Therefore, third side has to be less than the sum of the two sides. The third side is thus, less than 12 + 16 = 28 cm.
The side cannot be less than the difference of the two sides. Thus, the third side has to be more than 16 – 12 = 4 cm.
The length of the third side could be any length greater than 4 cm and less than 28 cm.

8. In a right angled triangle, the square on the hypotenuse = sum of the squares on the legs.
Here sum of the squares on the legs = square of 8 + square of 6 = 64 + 36 = 100
So length of hypotenuse = square root of 100 = 10 cm

9. Here square of hypotenuse = square of 25 = 25 x 25 = 625
Square of one leg = Square of 20 = 20 x 20 = 400
So length of the square of other leg = 625 – 400 = 225
Length of other leg = 15 cm.
Therefore, Perimeter = 15 + 15 + 20 + 20 = 70 cm.

10. Diagonals of a rhombus bisect each other at right angles. So there will be four equal triangles with legs 4 cm and 3cm.
So square of hypotenuse = square of 4 + square of 3 = 16 + 9 = 25 cm
Therefore, length of hypotenuse = 5 cm.
Perimeter = 5 + 5 + 5 + 5 = 20 cm.