1. Our Lesson
Polygons
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2. Warm up Find x Find y Find z Find w
In the given figure 1, AB || CD and AC || BD
Find x
Find y
In the given figure 2, l || m
Find z
Find w
Figure 1
Figure 2
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3. Lets recap what we have learned in the previous lesson
Parallel lines are two lines in a plane which do not meet even when produced indefinitely.
When a transversal cuts two parallel lines pairs, the sum of the interior angles on the same side of transversal is 180°.
When a transversal cuts two parallel lines pairs of corresponding angles are equal.
When a transversal cuts two parallel lines pairs of alternate interior angles are equal.
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4. Two lines are parallel if any one of the following conditions hold:
Pairs of alternate interior angles are equal.
Pairs of corresponding angles are equal.
The sum of the interior angles on the same side of transversal is 180°
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5. Let’s get started
Polygon: A polygon is a closed plane figure with three or more sides that are all straight. The sides do not cross each other. Two sides meet at every vertex.
Examples:
Triangle
Rectangle
Square
Pentagon
Hexagon
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6. Types of Polygons Concave polygon Convex polygon Regular polygon
Irregular polygon
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7. Concave polygon If a polygon has a reflex angle (A reflex angle is
greater than 180º and less than 360º) then it is said
to be a concave polygon.
Example:
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8. Convex polygon A polygon that has all interior angles less than 180°.
Every line segment between two vertices of the
polygon does not go exterior to the polygon.
Example:
Regular pentagon
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9. Regular polygon A regular polygon's sides are all of the same length
and its angles are the same size.
Examples:
Square
Equilateral Triangle
Regular hexagon
Regular octagon
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10. Irregular polygon
If a polygon is not a regular polygon, then it is said
to be an irregular polygon.
Example:
Quadrilateral
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11. Names of Polygons Name Sides Triangle 3 Quadrilateral 4 Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
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12. Quadrilateral Family Triangle Rectangle Square Parallelogram Pentagon
Trapezium
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13. Octagon
Hexagon
Heptagon
Nonagon
Decagon
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14. Diagonals of a polygon
A line segment connecting non-adjacent vertices of a polygon.
Polygon has n (n-3) diagonals. 2
diagonal
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15. Sum of Interior Angles of a Polygon
Formula to find Sum of interior angles of a given polygon:
Sum of Interior Angles= 180(n-2), n denotes
the number of sides
Note: Using the above formula, we can find the number of sides and the interior angles of a polygon.
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16. Each Interior Angle of a Regular Polygon
Let's state the general formula for finding each
interior angle of a REGULAR polygon
FORMULA: 
Each interior angle of a regular polygon = 180(n-2) ,
where n represents number of sides n
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17. Exterior Angles of a Polygon
An exterior angle of a polygon is formed by extending one side of the polygon. The sum of the exterior angles is ALWAYS equal to 360º.
Formula: 
Each exterior angle (regular polygon) = , where n represents number of sides n
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18. Examples What is the name of the polygon with sides 9. Nonagon
How many diagonals in a decagon?
Write the example of convex polygon. Regular pentagon
How do you find the number of sides from the formula sum of interior angles = 180(n-2) ? Solve for n
Find the sum of the exterior angles of nonagon? 
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19. Your Turn Name the polygon :
Write the number of sides of a polygon: Octagon -
Draw the diagram of the given polygon: Pentagon
Write polygon or not a polygon. Circle
Write the types of polygon.
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20. Your Turn 6. The sum of the exterior angles is ALWAYS equal to _____.
7. Find the sum of the exterior angles of a decagon.
8. Find the measure of each exterior angle of a regular hexagon.
9. Write the formula to find the sum of Interior angles of a polygon.
10. Write the example of irregular polygon.
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21. Refreshment Time
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22. Lets play a Game
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23. 1) Find the number of degrees in the sum of the interior angles of an Nonagon.
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24. 2) Each interior angle of a regular polygon measures 108
2) Each interior angle of a regular polygon measures 108.  How many sides does the polygon have ?
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25. 3) The measure of each exterior angle of a regular polygon is 45º
3) The measure of each exterior angle of a regular polygon is 45º.How many sides does the polygon have ?
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26. Lets review what we have learned in our lesson
Polygons: A polygon is a closed plane figure made up of 3 or more line segments.
Types of Polygons:
Concave, Convex, Regular and Irregular.
Names of Polygon according to the sides are Triangles, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon.
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27. Formulae Sum of Interior Angles= 180(n-2), n denotes
the number of sides
Each interior angle of a regular polygon = 180(n-2) where n represents number of sides n
Each exterior angle (regular polygon) = , where n represents number of sides n
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28. Do Practice the lesson surely
You did great in your lesson today !
Do Practice the lesson surely
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