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).
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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