Polygons The word polygon is a Greek word
- Slides: 46
Polygons The word ‘polygon’ is a Greek word. Poly means many and gon means angles.
Polygons • The word polygon means “many angles” • A two dimensional object • A closed figure Polygons
More about Polygons • Made up of three or more straight line segments • There are exactly two sides that meet at a vertex • The sides do not cross each other Polygons
Examples of Polygons
These are not Polygons
Terminology Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Polygons
Vertex Side Polygons
• Interior angle: An angle formed by two adjacent sides inside the polygon. • Exterior angle: An angle formed by two adjacent sides outside the polygon. Polygons
Exterior angle Interior angle Polygons
Let us recapitulate Exterior angle Vertex Side Diagonal Interior angle Polygons
Types of Polygons • Equiangular Polygon: a polygon in which all of the angles are equal • Equilateral Polygon: a polygon in which all of the sides are the same length Polygons
• Regular Polygon: a polygon where all the angles are equal and all of the sides are the same length. They are both equilateral and equiangular Polygons
Examples of Regular Polygons
A convex polygon: A polygon whose each of the interior angle measures less than 180°. If one or more than one angle in a polygon measures more than 180° then it is known as concave polygon. (Think: concave has a "cave" in it) Polygons
INTERIOR ANGLES OF A POLYGON Polygons
Let us find the connection between the number of sides, number of diagonals and the number of triangles of a polygon. Polygons
180 o 180 o 4 sides Quadrilateral 5 sides 2 x 180 o = 360 o 2 3 x 180 = 540 o 3 1 diagonal 180 o Pentagon o 2 diagonals 180 o 180 o 6 sides 4 Hexagon 4 x 180 o = 720 o 3 diagonals 7 sides 5 Polygons Heptagon/Septagon 5 x 180 o = 900 o 4 diagonals
Regular Polygon Triangle No. of sides No. of diagonals No. of 3 0 1 Polygons Sum of the interior angles 180 0 Each interior angle 0 180 /3 0 = 60
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 0 0 360 /4 0 = 90
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 0 360 /4 0 = 90 Pentagon 5 2 3 3 x 180 0 = 540 0 540 /5 0 = 108 Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 0 0
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 0 360 /4 0 = 90 Pentagon 5 2 3 3 x 180 0 = 540 0 540 /5 0 = 108 Hexagon 6 3 4 4 x 180 0 = 720 0 720 /6 0 = 120 Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 0
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 0 360 /4 0 = 90 Pentagon 5 2 3 3 x 180 0 = 540 0 540 /5 0 = 108 Hexagon 6 3 4 4 x 180 0 = 720 0 720 /6 0 = 120 Heptagon 7 4 5 5 x 180 0 = 900 0 900 /7 0 = 128. 3 Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 0 0
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 0 360 /4 0 = 90 Pentagon 5 2 3 3 x 180 0 = 540 0 540 /5 0 = 108 Hexagon 6 3 4 4 x 180 0 = 720 0 720 /6 0 = 120 Heptagon 7 4 5 5 x 180 0 = 900 0 900 /7 0 = 128. 3 “n” sided polygon n Association with no. of sides Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 Association with no. of triangles 0 0 Association with sum of interior angles
Regular Polygon No. of sides No. of diagonals No. of Triangle 3 0 1 180 Quadrilateral 4 1 2 2 x 180 0 = 360 0 360 /4 0 = 90 Pentagon 5 2 3 3 x 180 0 = 540 0 540 /5 0 = 108 Hexagon 6 3 4 4 x 180 0 = 720 0 720 /6 0 = 120 Heptagon 7 4 5 5 x 180 0 = 900 0 900 /7 0 = 128. 3 “n” sided polygon n n-3 n-2 (n - 2) 0 x 180 Polygons Sum of the interior angles 0 Each interior angle 0 180 /3 0 = 60 0 0 (n - 2) 0 x 180 / n
1 Calculate the Sum of Interior Angles and each interior angle of each of these regular polygons. 7 sides Septagon/Heptagon Sum of Int. Angles 900 o Interior Angle 128. 6 o 2 3 4 9 sides 10 sides 11 sides Nonagon Decagon Hendecagon Sum 1260 o I. A. 140 o Sum 1440 o I. A. 144 o Sum 1620 o I. A. 147. 3 o Polygons
Find the unknown angles below. w 75 o 2 x 180 o = 360 o 360 – 245 = 115 o 140 o x 100 o 70 o 125 o 100 o 115 o 3 x 180 o = 540 o 540 – 395 = 145 o 125 o z 138 o 133 o y 4 x 180 o = 720 o 720 – 603 = 117 o 95 o 110 o 121 o 117 o Diagrams not drawn accurately. 105 o 137 o 5 x 180 o = 900 o Polygons 900 – 776 = 124 o
EXTERIOR ANGLES OF A POLYGON Polygons
An exterior angle of a regular polygon is formed by extending one side of the polygo Angle CDY is an exterior angle to angle CDE B A C F 2 E 1 D Y Exterior Angle + Interior Angle of a regular polygon =180 Polygons 0
1200 600 600 1200 Polygons 1200
1200 Polygons
1200 Polygons
3600 Polygons
600 600 600 Polygons
600 600 600 Polygons
3 4 600 2 600 5 600 1 6 Polygons
3 4 600 2 600 5 600 1 6 Polygons
3 4 2 3600 5 1 6 Polygons
900 900 Polygons
900 900 Polygons
900 900 Polygons
2 3 3600 1 4 Polygons
No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to 360º. Sum of exterior angles = 360º Polygons
In a regular polygon with ‘n’ sides 0 Sum of interior angles = (n -2) x 180 i. e. 2(n – 2) x right angles 0 Exterior Angle + Interior Angle =180 0 Each exterior angle = 360 /n 0 No. of sides = 360 /exterior angle Polygons
Let us explore few more problems • Find the measure of each interior angle of a polygon with 9 sides. 0 • Ans : 140 • Find the measure of each exterior angle of a regular decagon. 0 • Ans : 36 • How many sides are there in a regular polygon if each interior angle measures 165 ? • Ans : 24 sides • Is it possible to have a regular polygon with an exterior angle equal to 40 ? • Ans : Yes 0 0 Polygons
Polygons DG
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