This won 2nd at cluster level and 1st at Regional level but unfortunately PPT Event was not scheduled for Nationals.

1. Prepared By:-
Muhammad
Sajeel Khan

2.  Polygons:- A simple closed curve made up of only line
segments is called a polygons.
 Curves that are polygons:-
 Curves that are not polygons:-

3. CLASSIFICATION OF POLYGONS
 Triangle:- 3 sides
 Quadrilateral:- 4 sides

4.  Pentagon:- 5 sides
 Hexagon:- 6 sides
 Heptagon:- 7 sides

5.  Octagon:- 8 sides
 Nonagon:- 9 sides
 Decagon:- 10 sides

6. DIAGONALS
 A diagonal is a line segment connecting
two non-consecutive vertices of a polygon.
 In 1st figure you can see that AC is the
diagonal, and in 2nd figure AD and BC.

7.  Convex Polygons:- Polygons that are convex
have no portions of their diagonals in their
exteriors.
 Concave Polygons:- Polygons that are concave
have portions of their diagonals in their exterior.

8.  Regular Polygons:- A regular polygon has both
equal sides and angles.
 Polygons that are not regular:-

9. ANGLE SUM PROPERTY
We all have used this property to find the
angles of a polygon.In it we first have to see
the number of sides of a polygon, then subtract
2 from it and multiply the result by 180 to find its
total angle sum.
Here is an example:-
Take Triangle, we know that it has 3 sides.
So, subtract 2 from it, and we get 1. And after
multiplying 1 with 180 we get 180 i.e. the
exact sum of the angles of a triangle.

10. Now we will take Pentagon. It has 5 sides, so
5 2 3. Then, 3 180 540.
So, sum of angles is equal to:-
No. of sides 2 180
For regular polygon interior angle plus exterior
angle is always equal to 180.

11.  Sum of the measures of the Exterior Angles of a
Polygon is always equal to 360.
In this we have got angles 110,50 & 90 and the
fourth angle is unidentified. But we know that all
exterior angles add up to 360. So,
110 50 90 x 360
250 x 360
x 360 250 ; x 110.

12. KINDS OF QUADRILATERALS:-
 Trapezium:- Trapezium is a quadrilateral with a
pair of parallel sides.
If the non-parallel sides of a trapezium are of
equal length, we call it an isosceles trapezium.

13.  Kite:- Kite is a special type of quadrilateral.
A kite has 4 sides.
There are exactly two distinct consecutive pairs
of sides of equal length.

14.  Parallelogram:- A parallelogram is a
quadrilateral whose opposite sides are parallel.

15. ELEMENTS OF A PARALLELOGRAM
 AB is parallel to DC and AD to BC.
 AB & DC are opposite sides.AD & BC form another pair of
opposite sides.
 angle A is opposite to angle C; angle D is opposite to angle
B.
 AB & BC are adjacent sides. This means, one of the sides
starts where the other one ends. So are BC & CD; CD &
DA.

16. PROPERTIES OF PARALLELOGRAM
 The opposite sides of a parallelogram are of
equal length.
 The opposite angles of a parallelogram are of
equal measure.
 The adjacent angles in a parallelogram are
supplementary(180).
 The diagonals of a parallelogram bisect each
other at the point of their intersection.

17. By Parallelogram Properties:-
 AB is equal to DC, so are AD & BC.
 angle A equals to angle C, and angle D is equal
to angle B.
 angle A plus angle B is 180, so are B & C, C &
D and D & A.
 Diagonals bisect each other. So, AE is equal to
CE and DE is equal to BE.

18. SOME SPECIAL PARALLELOGRAMS
 Rhombus:- A rhombus is a quadrilateral with
equal sides. It has all the properties of a
parallelogram and also that of a kite.
The diagonals of a rhombus are perpendicular
bisectors of one another.

19.  Rectangle:- A rectangle is a parallelogram with
equal angles. Being a parallelogram it has
opposite sides of equal length and its diagonals
bisect each other.
The diagonals of a rectangle are of equal
length.

20.  Square:- A square is rectangle with equal sides.
This means a square has all the properties of a
rectangle with an additional requirement that all
sides have equal length.
The square, like the rectangle, has diagonals
of equal length. In square the diagonals:-
bisect one another;
are of equal length;
are perpendicular to one another.