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 MATHEMATICS
Quadrilaterals – 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.
- 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.