Quadrilaterals

• Introduction•What is a Quadrilateral•Angle Sum Property of a Quadrilateral• Types of Quadrilaterals And Their Properties•Theorems

- Square- Rectangle- Rhombus- Parallelogram- Trapezium- Kite

•Mid-point Theorem And It’s Proof

Quadrilateral just means "four sides"(quad means four, lateral means side). Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2-dimensional.

A Quadrilateral is an enclosed 4 sided figure which has 4 vertices and 4 angles.

There are two types of quadrilaterals and they are:-

Convex quadrilateral:-

A quadrilateral whose all four angles sum upto 360 degree and diagonals intersect interior to it

Concave quadrilateral:-

A quadrilateral whose sum of four angles is more than 360 degrees and diagonals intersect interior to it.

There are many types of quadrilaterals which have many different properties.

Angle sum property of a

quadrilateral

The sum of all the angles of

a quadrilateral is 360˚. This is

the angle sum property of a

quadrilateral.

A quadrilateral with all congruent sides & each angle a right angle is called a Square.

Square has equal sides.

Opposite sides are parallel.

Every angle is right angle.

Diagonals are congruent.

Diagonalsbisect each other.

Each diagonalis perpendicu-lar bisector of the other.

A quadrilateral with each angle a right angle and opposite side congruent is called a .

• Every angle is right angle.• Opposite sides are congruent.• Opposites sides are parallel.• Diagonals are congruent .• Diagonals bisect each other.

A quadrilateral which has opposite

sides parallel is called a

parallelogram.

Diagonals bisect each

other

Opposite sides are parallel

Opposite angles are congruent

Opposite sides are

congruent

Only one pair of opposite side is

parallel.

KITEA quadrilateral in which there are two pairs of sides & each pair is made up of adjacent sides that are equal in length

is called kite.

PROPERTIES OF KITE

THEOREMS

A diagonal of a parallelogram divides it

into two congruent triangles.

In a parallelogram opposite sides are

equal.

If each pair of opposite sides of a

quadrilateral are equal, the it is a

parallelogram.

In a parallelogram opposite sides are

equal.

If in a quadrilateral, each pair of opposite

angles is equal, the it is a quadrilateral.

The diagonals of a parallelogram bisects

each other.

If the diagonals of a quadrilateral bisect

each other, then it is a parallelogram.

A quadrilateral is a parallelogram, If a pair

of opposite sides is equal and parallel.

Given:-D and E are the mid points of the sides AB and AC .

To prove:-DE is parallel to BC and DE is half of BC.

construction:- Construct a line parallel to AB through C.

proof:-in triangle ADE and triangle CFE

AE=CE

angle DAE= angle FCE (alternate angles )

angle AED= angle FEC (vertically opposite angles)

Therefore triangle ADE is congruent to triangle CFE

Hence by CPCT AD= CF- - - - - - - - -1

But

AD = BD(GIVEN)

so from (1), we get,

BD = CF

BD is parallel to CF

Therefore BDFC is a parallelogram

That is:- DF is parallel to BC and DF= BC

Since E is the mid point of DF

DE= half of BC, and , DE is parallel to BC

Hence proved .

To understand the mid-point

theorem well you can watch

the video on it on youtube by

Tanisha Garg.

MADE BY: TANISHA

YASHVI

GUARI

RADHA