This document defines and provides key information about different types of polygons. It discusses polygons in general, then focuses on quadrilaterals. It defines triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons. It then discusses properties of special quadrilaterals including parallelograms, rectangles, squares, rhombi, kites, and trapezoids. It provides the sufficient conditions to prove each type of polygon or quadrilateral and includes examples.

2. Polygons
Quadrilaterals
Sufficient
conditions
Polygons
Polygons
Sum of the interior angles of a polygon with n sides = (n – 2)180º
Sum of the exterioranglesof any polygon = 360º
A regular polygon is a polygon with equal sidesand therefore equal anglestoo.
Every interior angle of a regular polygon with nsides
360o
n
. Polygons
.
Important formulas concerning polygons:
n
Every exterior angle of a regular polygon with nsides
=
2
o
= (n 2)180

3. Names ofpolygons
Triangle (3sides)
Quadrilateral(4sides)
Pentagon(5sides)
Hexagon(6sides)
Heptagon(7sides)
Octagon (8sides)
Nonagon(9sides)
Decagon (10sides)
Example
Find the size of the angles indicated by letters:
FlashCard
Quadrilateral
4 sides, 4 angles
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Quadrilateral (4)
A Quad Bike has 4 wheels
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3

4. FlashCard
pentagon
5 sides, 5 angles
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pentagon
5 sides, 5 angles
Buckyball:
12 pentagons (see
black patches), 20
hexagons
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Hexagon
6 sides, 6 angles
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heXagon
6 sides, 6angles
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4
Think X: siX

5. FlashCard
hexagon
6 sides, 6angles
Buckyball:
12 pentagons, 20
hexagons (see white
patches)
FlashCard
heptagon
7 sides, 7 angles
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heptagon
7 sides, 7angles
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octagon
8 sides, 8 angles
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5

6. octagon
think octopus
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octagon
8 sides, 8angles
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4
Special Quadrilaterals
•TheParallelogram
A four-sided polygon with two pairs ofparallel
and equal sides.
•Rectangle: A rectangle is a parallelogram with
rightangles.
• Square: A square is a rectangle with 4 equalsides.
•Rhombus: A rhombus is a parallelogram with 4
equal sides.
Special Quadrilaterals
• Trapezium: A trapezium is a quadrilateral with only one pairof
parallel sides
• Kite: A quadrilateral in which two pairs of adjacent sides are
equal
The familytree
6

7. SpecialQuadrilaterals:properties
Example
Find the values of x
andy.
Given: AD║BC
Find the values of x
andy.
Exercise
Findx
Parallelogram
Sufficient conditions to provea
parallelogram
Prove one of the following:
• Both pairs of opposite sides parallel
• Both pairs of opposite sides equal
• Both pairs of opposite angles equal
• Diagonals bisect each other
• One pair of opposite sides parallel and
equal
7

8. Rectangle
Sufficient conditions to provea
rectangle
• Prove the quadrilateral
is a parallelogram AND
one interior angle
equals 𝟗𝟎°
Rhombus
Sufficient conditions to provea
rhombus
• Prove the quadrilateral
is a parallelogram AND
one pair of adjacent
sides are equal
Square
Sufficient conditions to provea
square
• Prove the
quadrilateral is a
parallelogram
AND one interior angle
equals 𝟗𝟎°
AND one pair of
adjacent sides is equal
8

9. Kite
Sufficient conditions to provea
kite
•Prove that two pairs
of adjacent sides are
equal
• Remember: NOT a
parallelogram
Trapezium
Sufficient conditions to provea
trapezium
•Prove that one
pair of opposite
sides are parallel
• Remember:
NOT a
parallelogram
Example:
ABCD is a parallelogram with DF = EB. Prove that AECF is a
parallelogram.
Complete the following statements:
9
2.
3.
4.
5.
1 If the diagonals of a quadrilateral are not equal, but
bisect each other perpendicularly, the quadrilateral
is a………
A triangle that has three equal sides is called an ….…
triangle.
If both pairs of adjacent sides of a quadrilateral are
equal, but the opposite sides are not equal, the
quadrilateral is a …….
If the diagonals of a quadrilateral are equal and
bisect each other perpendicularly, the quadrilateral
is a….…
If both pairs of opposite angles of a quadrilateral are
equal, the quadrilateral is a ……