K J Somaiya Comprehensive College of Education, Training & Research

Name : Monica PandaRoll No : 44Subject : MathematicsTopic : QuadrilateralsStandard : VII

Road Map

• Objective• Definition• Introduction• Properties• Evaluation

OBJECTIVE:

At the end of the lesson, the students should be able to know the properties of quadrilaterals

Definition• Polygon – a closed many straight-

sided figure.

triangle parallelogram

octagonheptagonhexagon

pentagon

Definition• Quadrilateral – a polygon with 4

angles and 4 straight sides.

Quadrilateral Family

parallelogram

rectangle

rhombus square

trapezoid

INTRODUCTION

• WORD QUADRILATERAL IS DERIVED FROM

TWO WORDS “QUADRI” MEANS “FOUR” AND

“LATERAL” MEANS “SIDES”.

8

Quadrilaterals

• A quadrilateral is a four-sided figure like the one shown. The sides are line segments connected together at their endpoints, called the vertices (plural of vertex) of the quadrilateral.

• A quadrilateral is named by its vertices.

• We call this quadrilateral ABCD or BADC or CDAB etc. (We start with a vertex and then proceed around the quadrilateral, either clockwise or counterclockwise.)

A

B

CD

* In quadrilateral ABCD, the vertices are A, B,C, and D* Adjacent vertices are :

A and BB and CC and DD and A

* Opposite vertices are :A and CB and D

A

B

CD

* Adjacent sides -Two sides with common vertex are :AB and BCBC and CDCD and DADA and AB

* Opposite sides are:AB and DCAD and BC

A

B

C

D

• Adjacent angles - Two angles with a common sides are: <A and <D<D and <C<C and <B<B and <A

• Opposite angles are :<A and <C<B and <D

AB

CD

• 4 vertices

A.

B.

C.

D.

• 4 sides• 4 angles

QUADRILATERALSQUADRILATERALS

Segments joining opposite vertices like AC and BD are called diagonals of the quadrilateral. There are 2

diagonals in a quadrilateral.

A

D C

B

QUADRILATERALSQUADRILATERAL

EXTERIOR OF

QUADRILATERAL

INTERIOR OF

QUADRILATERAL

A

B

CD

E.

.

..

.

. GH

F

J

I

PROPERTIES OF A QUADRILATERAL

• IF A LINE CONTAINING ANY ONE OF THE FOUR SEGMENTS PQ, QR, RS, QS IS DRAWN, THEN REMAINING TWO POINTS LIE ON THE SAME SIDE OF THIS LINE.

P

R

Q

S

• The sum of all the angles equals 360º degrees.

70º

110º

70º

110º

70º70º

110º110º+

360º

QUADRILATERALSEXPERIMENTEXPERIMENT

AIM:AIM: To verify that the sum of 4 angles of a quadrilateral is 360 degree.

1. Draw 2 [congruent] quadrilaterals of same shape and size.

QUADRILATERALS

2. Draw arcs of same radii at the 4 vertices of the quadrilateral.

3. Colour the region enclosed as shown in the figure.

QUADRILATERALS4. Glue the figure1 in the note book.

5. Separate the angles in figure2 by zig-zag lines as shown.

QUADRILATERALS6. Cut the 4 angles of figure2 as shown.

QUADRILATERALS

7. Arrange the angles and paste them side by side.OBSERVATIONS:

4-angles of quadrilateral can be assembled in to a circle.

4-angles of a quadrilateral gives a complete angle.

The sum total of the 4 angles of quadrilateral is 3600.

EVALUATION

• Examples of shapes or curves that are not classified as quadrilaterals. They do not follow the definition of a quadrilateral. Can you give a reason why?

Are They Quadrilaterals?

ACB

Observe the figure and answer the following questions:

1. Name the points in the interior of the quadrilateral PQRS ?

2. Name the points in the exterior of the quadrilateral PQRS ?

3. Name the points on the quadrilateral PQRS ?

VW

Y

XU

T.

. . ..

.

RS

QP

What is the missing angle?

81º58º

109º?

A

D C

B