Our Lesson Polygons Confidential

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 Confidential

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. Confidential

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

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 Confidential

Types of Polygons Concave polygon Convex polygon Regular polygon Irregular polygon Confidential

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: Confidential

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 Confidential

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

Irregular polygon If a polygon is not a regular polygon, then it is said to be an irregular polygon. Example: Quadrilateral Confidential

Names of Polygons Name Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Confidential

Quadrilateral Family Triangle Rectangle Square Parallelogram Pentagon Trapezium Confidential

Octagon Hexagon Heptagon Nonagon Decagon Confidential

Diagonals of a polygon A line segment connecting non-adjacent vertices of a polygon. Polygon has n (n-3) diagonals. 2 diagonal Confidential

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

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 Confidential

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

Examples What is the name of the polygon with sides 9. Nonagon How many diagonals in a decagon? 20 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? 360 Confidential

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. Confidential

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. Confidential

Refreshment Time Confidential

Lets play a Game www.miniclip.com/games/monkey-lander/en/ Confidential

1) Find the number of degrees in the sum of the interior angles of an Nonagon. Confidential

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 ? Confidential

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 ? Confidential

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

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

Do Practice the lesson surely You did great in your lesson today ! Do Practice the lesson surely Confidential