CLASS:- 9TH DIV:- B SCHOOL:- P.Dr. V.V.P.VIDYALAYA, LONI. CHAPTER 5 QUADRILATERALS CLASS:- 9TH DIV:- B SCHOOL:- P.Dr. V.V.P.VIDYALAYA, LONI.

Quadrilaterals The word Quadrilateral is derived from two words “ Quadri means Four” and Lateral means sides. In the following figures there are four coplanar points. B, H, I, R and four segments segment BH ,HI, IR & RB from different figures. (a,b,c,d,e) I R R (a) B R I B B H I R H I (b) (d) H (e) B R B H (c) H I Which of these figures are quadrilaterals?

The Diagonals of Quadrilateral always intersect in its interior Definition of Quadrilateral : The union of four segments namely seg PQ, seg QR, seg RS and seg SP is called Quadrilateral S R In this It is denoted by  PQRS & read as Quadrilateral PQRS. P Q Note:- Interior of the Quadrilateral is a convex set but Quadrilateral is not a convex set In short if P,Q,R & S are four coplanar points, such that no three of them are collinear and seg PQ, seg QR, seg RS & seg SP do not intersect each other except at their end points, then the figures so formed is known as Quadrilateral PQRS. The Diagonals of Quadrilateral always intersect in its interior

Complete the table, refer above figure Terms : related to Quadrilateral Elements Names of the elements Vertices Point k….. , ….., Sides Seg KA,……., ……. Angles AKJ, ……..,……. Diagonals seg………, seg……….. Pairs of Adjacent angles or Consecutive angles K and A, ……….. ……….., ………., Pair of Opposite sides Seg ……… , seg………… Pairs of Adjacent sides or Consecutive sides 1) Seg ……… , seg………… 2) Seg ……… , seg………… Pairs of Opposite angles ……….., ………….. ………...,………….. A K J I Complete the table, refer above figure

Types of Quadrilaterals & their properties 1. Parallelogram : Definition: A quadrilateral is called a parallelogram if its opposite sides are parallel A B D C Properties: The opposites sides of parallelogram are congruent. The opposites angles of parallelogram are congruent. The diagonals of a parallelogram bisect each other. Pair of opposite sides is parallel and congruent.

Every rectangle is parallelogram Definition: A parallelogram in which each angle is right angle is called Rectangle B A D C Properties: Diagonals of rectangle are congruent. Every rectangle is parallelogram

Every Rhombus is a Parallelogram. Definition: A quadrilateral having all sides congruent is called Rhombus. A B D C Properties: Diagonals of Rhombus are perpendicular bisectors of each other. Diagonals of Rhombus bisect of each other at right angle. Every Rhombus is a Parallelogram.

Every square is Rhombus. Definition: A quadrilateral having all its sides and angles are congruent is called square A B D C Properties: Diagonals of square are congruent. Diagonals of square are perpendicular bisectors of each other Every square is Rhombus.

5. Trapezium Definition: A quadrilateral is said to be a Trapezium, if only one pair of opposites sides is parallel B A D C Figure shows a Trapezium ABCD in which side AB side DC

6. Isosceles Trapezium Definition: Trapezium in which non parallel sides are congruent is called an Isosceles Trapezium B A D C Property: Diagonals of an Isosceles Trapezium congruent.

7. Kite A B D In  ABCD seg AB  seg AD seg CB  seg CD, Diagonal AC is perpendicular bisector of Diagonal BD Then ABCD is a kite. C

Isosceles Trapezium Rhombus Square

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