Quadrilateral

POWER POINT PRESENTATION

OF MATHS

Presented By : Ankit Kumar

sinha Class : 9th‘c’

TOPIC : QUADRILATERAL

What is a Quadrilateral?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.

Types of quadrilateral

A quadrilateral which has opposite sides parallel is called a parallelogram . Properties:-• A diagonal of a parallelogram divides it into two congruent triangles.•In a parallelogram, opposite sides are equal.•In a parallelogram opposite angles are equal.•The diagonals of a parallelogram bisect each other.•A quadrilateral with opposite sides parallel and equal is a parallelogramThese properties have their converse also.

Parallelogram and it’s properties

RECTANGLE AND IT’S PROPERTIESA rectangle is a parallelogram with all angle 90 degreeThe properties of rectangle are:-The diagonals of rectangle are of equal length.It has including properties of parallelogram. It has two pairs of opposite sides equal.The opposite sides of rectangle are parallel to each other.

SQUARE AND IT`S PROPERTIES

A square is a rectangle with adjacent sidesequal. The properties of a square are:-Square has including properties of RectangleDiagonals of a square bisect each other at 90 Degrees and are equal.The all four interior angles of square are right angles.

Rhombus and it’s propertiesA Rhombus is a parallelogram with adjacentsides equal. The properties of rhombus are:-A rhombus has the including properties of A parallelogram.The diagonals of rhombus bisect each other at 90 degreeThe diagonals of rhombus bisect opposite angles

TRAPEZIUM AND IT’S PROPERTIESA trapezium is quadrilateral with one pair of opposite sides parallel and other sides are non parallelPROPERTIES OF TRAPEZIUM ARE:-Co-interior angles of parallel sides of trapezium are supplementarySum of the angles of trapezium are 360 degree.

KITE AND IT’S PROPERTIESA quadrilateral with two pairs of adjacent sides equal is known as a kite. Properties of kite are:-The diagonals of a kite bisect each other 90 degree.Adjacent sides of a kite are equal.The smaller diagonal bisect the angles of kite.Sum of angles of kite is 360 degree.

Mid-point theorem:-The line segment joining the mid point of two sides of a triangle is always parallel to the third side and half of it.

Proof of mid point theorem

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- - - - - - - - -1But AD = BD(GIVEN) so from (1), we get,BD = CFBD is parallel to CF Therefore BDFC is a parallelogramThat 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 .

CONVERSE OF MID POINT THEOROM

According to the converse of mid point theorem the line drawn through the mid point of one side of a triangle, is parallel to another side bisects the third side.

WE CAN PROVE THE CONVERSE OF THE MID POINT THEOROM THROUGH THE EXPLANATION IN THE NEXT SLIDE .

and EF is half of BC