# Quadrilaterals – Class 9 Maths.

**Chapter 8 of NCERT/CBSE Class 9 Mathematics is about Quadrilaterals. Here you can find out practice problems for this chapter.**

**CBSE CLASS 9 MATHEMATICSQuadrilaterals – Chapter 8 / Sample papers.Fill in the blanks:**

- The sum of the angles of a quadrilateral is ———— degree.
- A ——— of a parallelogram divides it into two congruent triangles.
- ———- is a parallelogram in which diagonals are equal and bisect each other.
- The line segment joining the mid points of two sides of a triangle is parallel to the ——– side.
- A ———- is a parallelogram if a pair of opposite sides is equal and parallel.
**Answer the following:** - Write four properties of a parallelogram.
- The angles of a quadrilateral are 3x, 2x, 5x and 2x degrees. Find the measure of all angles?
- The angles of quadrilateral are in the ratio 1: 2: 3:4.Find all the angles of the quadrilateral
- Describe important properties of a square.
- If one angle of a quadrilateral is 120 degree and all the other three angles are equal. Find the measures of the equal angles of the quadrilateral.

**ANSWERS:**

- 360
- Diagonal
- Rectangle
- Third
- Quadrilateral
- In a parallelogram,

i) Opposite sides are equal.

ii) Opposite angles are equal.

iii) Diagonals bisect each other.

iv) A pair of opposite sides is equal and parallel. - We know that the sum of the angles of a quadrilateral is 360 degree.

Therefore, 3x + 2x + 5x + 2x = 360

12 x = 360

x = 360/12 = 30

So the four angles are 3x = 3 x 30 = 90 degree

2x = 2 x 30 = 60 degree

5x = 5 x 30 = 150 degree

2x = 2 x 30 = 60 degree. - Let the measure of the angles be x, 2x, 3x and 4x.

By Angle Sum Property of a quadrilateral, x + 2x + 3x + 4x = 360

10x = 360

x = 360/10 = 36 degree

Therefore, the four angles are x = 36 degree

2x = 2 x 36 = 72 degree

3x = 3 x 36 = 108 degree

4x = 4 x 36 = 144 degree. - Important properties of a square are:

i) All sides are equal

ii) All angles are equal to 90 degree.

iii) Diagonals are equal.

iv) Diagonals bisect each other at right angle.

v) Diagonals bisect the angles of vertex. - Let the equal angle be x.

Then by Angle sum property of quadrilateral, x + x + x + 120 = 360

3x + 120 = 360

3x = 360 – 120 = 240

x = 240/3 = 80

So the other three equal angles are 80 degree each.