NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 8

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8. Quadrilaterals

Quadrilaterals

S.no

Terms

Descriptions

1

Quadrilateral

A 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

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

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

2

Angle Property of Quadrilateral

1) Sum of all the interior angles is 360°

2) Sum of all the exterior angles is 360°

3

Parallelogram

A 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 divide into two congruent triangles

called a parallelogram

Called a Parallelogram

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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

4

Trapezium

A quadrilateral which has one pair of opposite sides parallel is called a trapezium.

called a trapezium

Called a Trapezium

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5

Rhombus

Rhombus 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

Rhombus is a Parallelogram

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6

Rectangles

A 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

Properties of a Rectangle

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7

Square

A quadrilateral, all of whose sides are equal and all of whose angles are right angles.

Properties of square are:

  • All the sides of a square are equal.

  • Each of the angles measures 9O.

  • 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

A Quadrilateral, All of Whose Sides Are

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8

Important 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.

9

Mid-point Theorems for Triangles

1)The line segment joining the mid-points of the

two sides of the triangle is 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