NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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8. Quadrilaterals

Quadrilaterals
S. noTermsDescriptions
1QuadrilateralA quadrilateral is the union of four line-segments determined by four distinct coplanar points of which no three are collinear and the line-segments intersect only at end points.

For ABCD to be quadrilateral, following condition are required

(a) The four points A, B, C and D must be distinct and co-planar.

(b) No three of points A, B, C and D are co-linear.

(c) Line segments i.e.. . , AB, BC, CD, DA intersect at their end points only.

A Quadrilateral

A quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilaterals.

The five most common types are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus

2Angle Property of Quadrilateral(1) Sum of all the interior angles is 360°

(2) Sum of all the exterior angles is 360°

3ParallelogramA quadrilateral which has both pairs of opposite sides parallel is called a parallelogram.

its properties are:

  • The opposite sides of a parallelogram are equal.
  • The opposite angles of a parallelogram are equal.
  • The diagonals of a parallelogram bisect each other.
  • The diagonal of a parallelogram divides into two congruent triangles
Called a Parallelogram

A quadrilateral is said to a parallelogram if Opposite sides are equal OR Opposite angles are equal OR Diagonal bisects each other OR A pair of opposite are parallel and equal

4TrapeziumA quadrilateral which has one pair of opposite sides parallel is called a trapezium.
Called a Trapezium
5RhombusRhombus is a parallelogram in which any pair of adjacent sides is equal.

Properties of a rhombus:

  • All sides of a rhombus are equal
  • The opposite angles of a rhombus are equal
  • The diagonals of a rhombus bisect each other at right angles.
Rhombus is a Parallelogram
6RectanglesA parallelogram which has one of its angles a right angle is called a rectangle.

Properties of a rectangle are:

  • The opposite sides of a rectangle are equal
  • Each angle of a rectangle is a right-angle.
  • The diagonals of a rectangle are equal.
  • The diagonals of a rectangle bisect each other.
Properties of a Rectangle
7SquareA quadrilateral, all whose sides are equal and all whose angles are right angles.

Properties of square are:

  • All the sides of a square are equal.
  • Each of the angle՚s measures 90.
  • The diagonals of a square bisect each other at right angles.

The diagonals of a square are equal.

A Quadrilateral, All of Whose Sides Are
8Important points about quadrilaterals(a) A square is always a parallelogram.

(b) A square is always a rectangle.

(c) A rhombus can be square.

(d) A rectangle has four right angles.

9Mid-point Theorems for Triangles(1) The line segment joining the mid-points of the

two sides of the triangle are parallel to the third

side

(2) A line drawn through mid-point of one side of a triangle and parallel to another side bisect the third side of the triangle