Quadrilaterals
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Transcript of Quadrilaterals
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• Introduction•What is a Quadrilateral•Angle Sum Property of a Quadrilateral• Types of Quadrilaterals And Their Properties•Theorems
- Square- Rectangle- Rhombus- Parallelogram- Trapezium- Kite
•Mid-point Theorem And It’s Proof
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Quadrilateral just means "four sides"(quad means four, lateral means side). Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2-dimensional.
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A Quadrilateral is an enclosed 4 sided figure which has 4 vertices and 4 angles.
There are two types of quadrilaterals and they are:-
Convex quadrilateral:-
A quadrilateral whose all four angles sum upto 360 degree and diagonals intersect interior to it
Concave quadrilateral:-
A quadrilateral whose sum of four angles is more than 360 degrees and diagonals intersect interior to it.
There are many types of quadrilaterals which have many different properties.
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Angle sum property of a
quadrilateral
The sum of all the angles of
a quadrilateral is 360˚. This is
the angle sum property of a
quadrilateral.
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A quadrilateral with all congruent sides & each angle a right angle is called a Square.
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Square has equal sides.
Opposite sides are parallel.
Every angle is right angle.
Diagonals are congruent.
Diagonalsbisect each other.
Each diagonalis perpendicu-lar bisector of the other.
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A quadrilateral with each angle a right angle and opposite side congruent is called a .
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• Every angle is right angle.• Opposite sides are congruent.• Opposites sides are parallel.• Diagonals are congruent .• Diagonals bisect each other.
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A quadrilateral which has opposite
sides parallel is called a
parallelogram.
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Diagonals bisect each
other
Opposite sides are parallel
Opposite angles are congruent
Opposite sides are
congruent
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Only one pair of opposite side is
parallel.
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KITEA quadrilateral in which there are two pairs of sides & each pair is made up of adjacent sides that are equal in length
is called kite.
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PROPERTIES OF KITE
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THEOREMS
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A diagonal of a parallelogram divides it
into two congruent triangles.
In a parallelogram opposite sides are
equal.
If each pair of opposite sides of a
quadrilateral are equal, the it is a
parallelogram.
In a parallelogram opposite sides are
equal.
If in a quadrilateral, each pair of opposite
angles is equal, the it is a quadrilateral.
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The diagonals of a parallelogram bisects
each other.
If the diagonals of a quadrilateral bisect
each other, then it is a parallelogram.
A quadrilateral is a parallelogram, If a pair
of opposite sides is equal and parallel.
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Given:-D and E are the mid points of the sides AB and AC .
To prove:-DE is parallel to BC and DE is half of BC.
construction:- Construct a line parallel to AB through C.
proof:-in triangle ADE and triangle CFE
AE=CE
angle DAE= angle FCE (alternate angles )
angle AED= angle FEC (vertically opposite angles)
Therefore triangle ADE is congruent to triangle CFE
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Hence by CPCT AD= CF- - - - - - - - -1
But
AD = BD(GIVEN)
so from (1), we get,
BD = CF
BD is parallel to CF
Therefore BDFC is a parallelogram
That is:- DF is parallel to BC and DF= BC
Since E is the mid point of DF
DE= half of BC, and , DE is parallel to BC
Hence proved .
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To understand the mid-point
theorem well you can watch
the video on it on youtube by
Tanisha Garg.
MADE BY: TANISHA
YASHVI
GUARI
RADHA
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