A quadrilateral is a four-sided polygon with four angles. There are different kinds of quadrilaterals including parallelograms, rectangles, squares, rhombi, kites, and trapezoids. Each kind has distinct properties - for example, a parallelogram has opposite sides that are parallel and opposite angles that are equal, while a rectangle has four right angles and diagonals that bisect each other. The document also discusses the mid-point theorem, which states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

1. QuadrilateralQuadrilateral

2. What isWhat is
quadrilateral?quadrilateral?
 A A quadrilaterquadrilater
alal is a four-is a four-
sided polygonsided polygon
with fourwith four
angles.angles.
 There areThere are
many kindsmany kinds
ofof
quadrilateraquadrilatera

3. Kinds ofKinds of
QuadrilateralQuadrilateral
 ParallelogramParallelogram
 RectangleRectangle
 SquareSquare
 RhombusRhombus
 KiteKite
 TrapeziumTrapezium

4. Properties ofProperties of
kinds ofkinds of
quadrilateralquadrilateral

5. ParallelograParallelogra
mm

6.  Meaning – AMeaning – A
quadrilateral with eachquadrilateral with each
pair of opposite sidespair of opposite sides
parallel.parallel.
 PropertiesProperties
1.1. Opposite sides are equal.Opposite sides are equal.
2.2. Opposite angles areOpposite angles are
equal.equal.
3.3. Diagonals bisect oneDiagonals bisect one
another.another.
4.4. Each diagonal of aEach diagonal of a
parallelogram separatesparallelogram separates

7. RectanglRectangl
ee

8.  Meaning ~ AMeaning ~ A
parallelogram with aparallelogram with a
right angle.right angle.
 PropertiesProperties
1.1. Opposite sides are equal.Opposite sides are equal.
2.2. Opposite angles areOpposite angles are
equal.equal.
3.3. Diagonals bisect oneDiagonals bisect one
another.another.
4.4. Each of the angle is aEach of the angle is a

9. SquareSquare

10.  Meaning ~ A rectangleMeaning ~ A rectangle
with sides of equalwith sides of equal
length.length.
 PropertiesProperties
1.1. Opposite sides are equal.Opposite sides are equal.
2.2. Opposite angles areOpposite angles are
equal.equal.
3.3. Diagonals bisect oneDiagonals bisect one
another.another.
4.4. Diagonals areDiagonals are
perpendicular to eachperpendicular to each

11. RhombusRhombus

12.  Meaning ~ AMeaning ~ A
parallelogram with sidesparallelogram with sides
of equal length.of equal length.
 PropertiesProperties
1.1. Opposite sides are equal.Opposite sides are equal.
2.2. Opposite angles areOpposite angles are
equal.equal.
3.3. Diagonals bisect oneDiagonals bisect one
another.another.
4.4. Diagonals areDiagonals are
perpendicular to eachperpendicular to each

13. KiteKite

14.  Meaning ~ A quadrilateralMeaning ~ A quadrilateral
with exactly two pairs ofwith exactly two pairs of
equal consecutive sides.equal consecutive sides.
 PropertiesProperties
1.1. The diagonals areThe diagonals are
perpendicular to oneperpendicular to one
another.another.
2.2. One of the diagonalsOne of the diagonals
bisects the other.bisects the other.
3.3. In the figure mLB = mLDIn the figure mLB = mLD
but mLA is not equal tobut mLA is not equal to
mLCmLC

15. TrapeziuTrapeziu
mm

16.  Meaning ~Meaning ~ AA
quadrilateral with onequadrilateral with one
pair of parallel sides.pair of parallel sides.
 PropertiesProperties
1.1. The diagonals of areThe diagonals of are
equal in length.equal in length.

17. Mid-PointMid-Point
TheoremTheorem
The segmentThe segment
joining thejoining the
midpoints of twomidpoints of two
sides of a trianglesides of a triangle
is parallel to theis parallel to the
third side and halfthird side and half
of it.of it.

18. ProveProve
 AM=BM [midpoint].AM=BM [midpoint].
 < AMP = <MBQ< AMP = <MBQ
[Corresponding angles for[Corresponding angles for
parallel lines cut by anparallel lines cut by an
transversal].transversal].
 <BQM=<QCP=<APM<BQM=<QCP=<APM
[Corresponding angles for[Corresponding angles for
parallel lines cut by anparallel lines cut by an
transversal].transversal].

19.  <BMQ=<MAP [When 2<BMQ=<MAP [When 2
pairs of correspondingpairs of corresponding
angles are congruent in aangles are congruent in a
triangle, the third pair istriangle, the third pair is
also congruent.]also congruent.]
 AMP is congruent toAMP is congruent to
MBQ. [ASA]MBQ. [ASA]
 Therefore: AP=MQ=PCTherefore: AP=MQ=PC
and MP=BQ=QC. and MP=BQ=QC.

21. By: Shefali KumarBy: Shefali Kumar
Class: IX-BClass: IX-B
School: RamagyaSchool: Ramagya
School, Sector-50,School, Sector-50,
NoidaNoida
Roll No.: 29Roll No.: 29