The E Tutor - Types of Quadrilaterals

8/2/2019 The E Tutor - Types of Quadrilaterals

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WHAT AREQUADRILATERALS?

A quadrilateral is a four-sided

polygon.

If sides are parallel, the distancebetween them is constant, and

they will never cross, even if

extended.


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SIX TYPES OF

QUADRILATERALS

RECTANGLE

SQUARE

PARALLELOGRAM

RHOMBUS

KITE

TRAPEZOID


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A RECTANGLE IS

A quadrilateral having two pairs of equalsides that are parallel

Sides meet at right angles (90)

Diagonals are equal in length


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RECTANGLE In a rectangle the diagonals, besides being equal in length

bisect each other.Given: ABCD is a Rectangle the diagonals are AC & BD

Bisect each other at a Point O.

To Prove: (i) AC = BD

(ii) OA = OC or OB = OD

Proof: In ABC and ABD

AB = AB --------- (Common)

BC = AD ---------------------(Apposite sides ABCD) A = B = 90 (angles of the rectangles)

ABC ABD S. A. S. Rule

So, AC = BD Proved

A B

CD

O


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RECTANGLE(ii) OA = OC or OB = OD

Proof: In AOB and COD

AB = CD (Sides of the ABCD)

AB || CD and transversal AC & BD

Then, ODC = OBA

And OCD = OAB

Alternate interior angles

AOB COD --- A. S. A Rule

So that all congruent part are equal .OA = OC

and OB = OD

Proved

A B

CD

O


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A SQUARE IS

A rectangle having all sides of equallength


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SQUARE

The diagonals of a square are perpendicular bisectors ofeach other

Given: ABCD is a Square, Where AC and BD is a diagonalbisect each other at a Pont O

To Prove: AOD = COD = 90

Proof: In AOD and COD

OD Common & OA =OC

AD = DC ------ Two sides of Squire

So, (By SSS) AOB COD, AOD = COD

Since AOD and COD are a linear pair,

AOD = COD = 90

A B

CD

O


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PARALLELOGRAM

A quadrilateral having two pairs of equalsides that are parallel

Opposite angles are equal

Diagonals are not equal in length


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PARALLELOGRAM

The diagonals of a parallelogram bisect each otherGiven: ABCD is a parallelogram where AC and BD is a diagonal

bisect each other at Point O

To Prove: AO = OC or BO= OD

Proof: In AOB and CODAB = CD

AB || CD

CDO = OBA

And DCO = OAB ------------ Alternate interior angles

So, AOB COD, then

AO = OC or BO =OD Proved

A B

CD

O


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A RHOMBUS IS

A parallelogram having all sides of equallength


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RHOMBUS The diagonals of a rhombus are perpendicular

bisectors of one another.Given: ABCD is a rhombus. Therefore it is a parallelogram too.

Since diagonals bisect each other,

OA = OC and OB = OD.

To Prove: AOD = COD = 90

Proof: In AOD and COD

OD Common & OA =OC --Given

AD = DC ------ Two sides of this rhombus

So, (By SSS) AOB COD, then AOD = COD,

Since AOD and COD are a linear pair,

AOD = COD = 90

A B

CD

O


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KITE A quadrilateral having two pairs of equal sides

One pair of opposite equal angles

One diagonal bisects the other.

Diagonals intersect at right angles.
http://www.mathsteacher.com.au/year7/ch08_angles/01_ang/ang.htmhttp://www.mathsteacher.com.au/year7/ch08_angles/01_ang/ang.htm


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TRAPEZOID

A quadrilateral with one pair of parallelsides


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The E Tutor - Types of Quadrilaterals

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