properties of quadrilaterals

2. • Introduction
•What is a Quadrilateral
•Angle SumPropertyof a Quadrilateral
• Types of Quadrilaterals And Their
Properties
•Theorems
- Square
- Rectangle
- Rhombus
- Parallelogram
- Trapezium
- Kite
•Mid-point TheoremAnd It’s Proof

3. 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.

4. A Quadrilateral is an
enclosed 4 sided figure which
has 4 vertices and 4 angles.
There are many types of quadrilaterals which
have many different properties.

5. 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.

7. A quadrilateral which has
opposite sides parallel is
called a parallelogram.

8. Diagonals
bisect each
other
Opposite
sides are
parallel
Opposite
angles are
congruent
Opposite
sides are
congruent

9. A quadrilateral with each
angle a right angle and
opposite side congruent is
called a .

10. • Every angle is right angle.
• Opposite sides are congruent.
• Opposites sides are parallel.
• Diagonals are congruent .
• Diagonals bisect each other.

13. A quadrilateral with all
congruent sides & each
angle a right angle is called
a Square.

14. Square has
equal sides.
Opposite
sides are
parallel.
Every angle is
right angle.
Diagonals are
congruent.
Diagonals
bisect each
other.
Diagonal
are
perpendicular

18. Only one pair of
opposite side is
parallel.

19. A pair of parallel sides. Called an
Isosceles trapezoid when the sides
that aren't parallel are equal in
length and both angles coming from
a parallel side are equal.
Isosceles Trapezoid

21. KITE
A 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.

22. PROPERTIES
OF KITE

23. THEOREM
S

24.  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, then 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.

25. 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.

28. 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

29. 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 .