MATHEMATICS

Chapter 8Quadrilatera

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Quadrilateral – The word ‘quad’ means four and the word ‘lateral’ means sides. - It is a figure bounded by four line segments such that no three of them are parallel to each other - It has four sides, vertices, and angles

SOME IMPORTANT DEFINITIONS:-

a) Adjacent sides- also known as consecutive sides - two sides of quadrilateral with common vertex

b) Opposite sides- two sides of quadrilateral with no common end- point

c) Adjacent angles- also known as consecutive angles - two angles of a quadrilateral with common arm

d) Opposite angles- two angles of a quadrilateral with no common arm

Trapezium Kite

Rhombus

Square

Parallelogram

Rectangle

Types of Quadrilaterals

Let us discuss about various kinds of quadrilaterals briefly:-

TRAPEZIUM A quadrilateral with one pair of parallel sides

ISOSCELES TRAPEZIUM A trapezium with non parallel sides as equal

TRAPEZIUM ISOSCELES TRAPEZIUM

PARALLELOGRAM A quadrilateral with both pairs of opposite sides equal

RHOMBUS A parallelogram with all sides equal

RECTANGLE A parallelogram whose each angle is right angle

SQUARE A rectangle with pair of adjacent sides equal

KITE A quadrilateral with two pairs of equal adjacent sides and unequal opposite sides

Let us discuss about various types of quadrilaterals in detail !!!

*RECTANGLE opposite sides are parallel and equal all angles are right angles diagonals are equal diagonals bisect each other

*SQUARE all sides are equal all angles are right angles opposite sides are parallel diagonals are equal diagonals bisect each other at right angles diagonals are perpendicular to each other

*RHOMBUS opposite sides are parallel all sides are equal opposite angles are equal diagonals bisect each other diagonals are perpendicular to each other

*KITE two pairs of equal adjacent sides

*PARALLELOGRAM opposite sides are equal opposite angles are equal diagonals bisect each other diagonals divide it into two congruent triangles bisect of any two consecutive angles intersect at right angle its angle bisectors form a rectangle

*TRAPEZIUM one pair of opposite sides are parallel(Isosceles Trapezium has non- parallel sides equal to each other)

ANGLE SUM PROPERTY OF A QUADRILATERAL

This property states that sum of four angles of a quadrilateral is 360.A B

C D

PROOF: IN ABD and ACD sum of angles =180*+180*=360* [ angle sum property of a triangle ]Hence, proved.

THANK YOU BY- RADHIKA GUPTA