Post on 18-Jan-2016
Confidential 1
Confidential 2
In the given figure 1, AB || CD and AC || BD
1) Find x Answer= 40°
2) Find y Answer= 35°
In the given figure 2, l || m
3) Find x Answer= 135°
4) Find y Answer= 135°
5) Find z Answer= 45°
6) Find w Answer= 45°
Figure 1
Figure 2
Warm up
Confidential 3
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.
Lets recap what we have learned in the previous lesson
Confidential 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°
Confidential 5
Let’s get startedPolygon: 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:
1. Triangle
2. Rectangle
3. Square
4. Pentagon
5. Hexagon
Confidential 6
Types of Polygons
Concave polygon
Convex polygon
Regular polygon
Irregular polygon
Confidential 7
Concave polygon
If a polygon has a reflex angle (A reflex angle isgreater than 180º and less than 360º) then it is saidto be a concave polygon.
Example:
Confidential 8
Convex polygon
A polygon that has all interior angles less than 180°.Every line segment between two vertices of thepolygon does not go exterior to the polygon.
Example:
Regular pentagon
Confidential 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
Confidential 10
Irregular polygon
If a polygon is not a regular polygon, then it is saidto be an irregular polygon.
Example:
Quadrilateral
Confidential 11
Names of Polygons
Name Sides
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Confidential 12
Triangle
Quadrilateral Family
Pentagon
Rectangle Square
Parallelogram Trapezium
Confidential 13
Hexagon Heptagon Octagon
Nonagon
Decagon
Confidential 14
Diagonals of a polygon
A line segment connecting non-adjacent vertices of a polygon.
Polygon has n (n-3) diagonals.
2
diagonal
Confidential 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.
Confidential 16
Each Interior Angle of a Regular Polygon
Let's state the general formula for finding eachinterior angle of a REGULAR polygon
FORMULA:
Each interior angle of a regular polygon = 180(n-2) ,
where n represents number of sides. n
Confidential 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) = 360 ,
where n represents number of sides. n
Confidential 18
Examples
1)What is the name of the polygon with sides 9. Nonagon
2)How many diagonals in a decagon? 20
3)Write the example of convex polygon. Regular pentagon
4) How do you find the number of sides from the formula sum of interior angles = 180(n-2) ? Solve for n
5)Find the sum of the exterior angles of nonagon? 360
Confidential 19
Your Turn
1. Name the polygon : Hexagon
2. Write the number of sides of a polygon: Octagon -
8
3. Draw the diagram of the given polygon: Pentagon
4. Write polygon or not a polygon. Circle Not a
polygon
5. Write the types of polygon. Concave, Convex,
Regular and Irregular
Confidential 20
Your Turn
6. The sum of the exterior angles is ALWAYS equal
to _____. 360 degree
7. Find the sum of the exterior angles of a decagon. 360 degree
8. Find the measure of each exterior angle of a regular hexagon. 60 degree
9. Write the formula to find the sum of Interior angles of a polygon. 180(n-2)
10. Write the example of irregular polygon. Quadrilateral
Confidential 21
Refreshment Time
Confidential 22
Lets play a Game
www.miniclip.com/games/monkey-lander/en/
Confidential 23
1) Find the number of degrees in the sum of the interior angles of an Nonagon. Solution:
An Nonagon has 9 sides. So n = 9.
Using our formula from above, that gives us 180(9-2)
= 180(7)
= 1260.
Confidential 24
2) Each interior angle of a regular polygon measures 108. How many sides does the polygon have ? First, set the formula (for each interior angle)
equal to the number of degrees given.
180(n-2) / n = 108
Cross multiply, 108n = 180(n-2)
Multiply 180 by (n-2), 108n = 180n – 360
Subtract 180n on both sides -72n = -360
Divide both sides by -72, n = 5
Confidential 25
3) The measure of each exterior angle of a regular polygon is 45º.How many sides does the polygon have ?
Set the formula equal to 45. 360/ n = 45
Cross multiply and solve for n. 360 = 45 n
n = 8
Confidential 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.
Confidential 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) = 360 , where n represents number of sides. n
Confidential 28
You did great in your lesson today !
Do Practice the lesson surely