its about mid-point theorem of chapter quadrilaterals of grade 9 of cbse board

2. • 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

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 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.

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

8. Square has
equal sides.
Opposite
sides are
parallel.
Diagonals are
congruent.
Every angle is
right angle.
Diagonals
bisect each
other.
Each diagonal
is perpendicu-lar
bisector of
the other.

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
which has opposite
sides parallel is
called a
parallelogram.

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

16. Only one pair of opposite side is
parallel.

17. 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.

18. PROPERTIES
OF KITE

19. THEOREMS

20.  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.

21.  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.

23. 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

24. 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 .

25. 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