Quadrilaterals Final

8/14/2019 Quadrilaterals Final

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What is a Quadrilateral?What is a Quadrilateral?

A quadrilateral is a two-dimensional figureformed by connecting four segmentsendpoint to endpoint with each segmentintersecting exactly two others. It alsohas four sides and four angles.


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ObjectivesObjectives

Make distinct definitions of whatparallelograms, kites,rectangles, squares, rhombi,

and trapezoids are. Sort and classify quadrilaterals.

Designate the best name for a

given quadrilateral, givenexamples.


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Terms associated withTerms associated withquardilateral.quardilateral.

Adjacent sides: Two sides of quardilateral areadjacent , if they have a common vertex.

Opposite sides: Two sides of a quardilateralare opposite sides , if they have no commonvertex.

Consecutive angels: The consecutive angelsof a quardilateral are two angels which

include a side in their intersection. In otherwords two angels are consecutive , if theyhave common arm.

Opposite angels: Two angels are said to be

opposite , if they do not have any common


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Are TheyAre They

Quadrilaterals?Quadrilaterals?

Examples of shapes or curves thatare not classified as quadrilaterals.

They do not follow the definition ofa quadrilateral. Can you give areason why?

A

CB


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Classification ofClassification of

QuadrilateralsQuadrilaterals A concave

quadrilateralcontains at

least oneangle that is>180o.

A quadrilateral is

convexif eachvertex lies inthe interior ofthe opposite

angle.


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Types of QuadrilateralsTypes of Quadrilaterals

Trapezoid

Parallelogram

Square

Rectangle Kite, Dart

Rhombus

Rectangle


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Parallelogram

Trapezoid

Rhombus

Rectangle

Square


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Name thatName that

Quadrilateral!Quadrilateral! A square is a

quadrilateralwith all sides

and anglesequal.

If allquadrilaterals

have 360o

total, what isthe angle ofeach vertexin a square?


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Name thatName that

Quadrilateral!Quadrilateral! A quadrilateral

with all angles

equal is arectangle.

A quadrilateralwith all sidesequal is arhombus.


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Name thatName that

Quadrilateral!Quadrilateral!

A quadrilateral with at least onepair of parallel sides is atrapezoid.


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Name thatName that

Quadrilateral!Quadrilateral! A quadrilateral with

both pairs ofopposite sides

parallel and equalin length is knownas aparallelogram.

oPa ra lle logra m s ca n b e cons ide re d sp e c ia lca se s o f t ra pe zo ids , s ince the y ha ve a

le a st on e pa ir of p a ra lle l s ide s .


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Name thatName that

Quadrilateral!Quadrilateral! A quadrilateralwith twoseparatepairs of equal

adjacentsides iscommonlycalled a kite.

However, if thekite isconcave, adartis a moreappropriate

term.


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NOW WE WILL LEARNNOW WE WILL LEARNTO IDENTIFYTO IDENTIFY

QUADRILATERALS BY:QUADRILATERALS BY:

and the length of theirsides.

their angles


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SquareSquare A square has four sides that are each the same

length. It also has four right angles (perfect corners).

1

23

4


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RhombusRhombus A rhombus has four sides that are each the same

length. But it has two acute and two obtuse angles.

acute

acuteobtuse

obtuse

S d


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Square andSquare and

RhombusRhombus A square and a rhombus both have four sides

that are the same length. So, how are theydifferent?

S d


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Square andSquare and

RhombusRhombus A rhombus can be thought of as a slanted

square.

If we push on the left-hand side of this square, itmight end up looking like

a rhombus.


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THE ONLY DIFFERENCETHE ONLY DIFFERENCEBETWEEN A SQUAREBETWEEN A SQUARE

AND A RHOMBUS IS INAND A RHOMBUS IS IN

THEIRTHEIR ANGLESANGLES..


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TrapezoidTrapezoid A trapezoid has four sides. Two sides are parallel. The opposing two sides are not parallel.

Those areparallel.

Those arenot parallel.


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Rectangle

A rectangle has foursides two long sides andtwo short sides.

Two sides are parallel.

The opposing two sides

are also parallel.

It also has four rightangles.


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ParallelogramA parallelogram has foursides two long sides andtwo short sides.

Two sides are parallel.

The opposing two sidesare also parallel.

But, it has two acute andtwo obtuse angles.


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Rectangle andRectangle and

ParallelogramParallelogram A parallelogram can be thought of as a slanted

rectangle.

If we push on the left-hand side of thisrectangle, it might end up looking like

a parallelogram.


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THE ONLY DIFFERENCETHE ONLY DIFFERENCEBETWEEN A RECTANGLEBETWEEN A RECTANGLEAND A PARALLELOGRAMAND A PARALLELOGRAM

IS THEIRIS THEIR ANGLESANGLES..


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We can use the followingWe can use the followingtable to make comparisonstable to make comparisons

between the quadrilaterals.between the quadrilaterals.

For example, what do aFor example, what do a

square and a rectangle havesquare and a rectangle havein common?in common?

d il lQ d il t l


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QuadrilateralsQuadrilateralsSHAPE SIDES ANGLES PARALLEL

LINES

Square 4 samelength

4 right angles 2 sets

Rhombus 4 samelength

2 acute2 obtuse

2 sets

Trapezoid different

lengths

different

angles

1 set

Rectangle 2 long, 2short

4 right angles 2 sets

Parallelogram 2 long, 2short

2 acute 2obtuse

2 sets


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VARIOUS THEOREMS INVARIOUS THEOREMS IN

QUARDILATERALSQUARDILATERALS(parallelogram)(parallelogram)..q The sum of four angels of a quardilateral is 360 degrees.

q A diagonal of a parallelogram divides it into two congurenttriangels.

q Diagonals of a parallelogram bisects each other.

q In a parallelogram , opposite sides are equal.

q Opposite angels of a parallelogram are equal.

q In a parallelogram , the bisectors of any two consecutive angels

intersect at right angel.q The angle bisector of a parallelogram form a triangle.

q If diagonals of a parallelogram bisects one of the angels of theparallelogram , it also bisects the second angle.

q If the diagonals of a parallelogram ABCD intersect at O and a linethrough O intersects AB at X & DC at Y , then OX=OY.


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QUADRILATERALSQUADRILATERALSAvni Singh

IX-A

INDIRAPURAM PUBLIC SCHOOL

6, NYAY KHAND-I, INDIRAPURAM, GHAZIABAD 201012

Quadrilaterals Final

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