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Download Polygons - Souderton Math
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Section 3.4 Exploring Polygons Thompson •Convex vs. Concave Polygons •Parts of a Polygon •Classifying Polygons •W/ some triangle review Exploring Polygons are many-sided figures, with sides that are line segments. Polygons are named according to the number of sides and angles they have. Can be “regular” – all sides and all angles are equal to each other Two sides of equal length Three acute angles Sum of angles = 180° All sides equal length Three acute angles Sum of angles = 180° Is a regular polygon No sides are equal No angles are equal May have obtuse angle Sum of angles = 180° Opposite sides are parallel Opposite side are equal in length Each angle equals 90° Sum of angles = 360° All sides equal All angles equal and are 90 ° each Sum of angles = 360 ° Is a regular polygon Two sides are parallel Has obtuse and acute angles Sometimes has a right angle Sum of angles = 360 ° All four sides of equal length Opposite angles are equal – 2 acute angles, 2 obtuse angles Sum of angles = 360 ° Regular polygon Opposite sides parallel Opposite sides equal in length Opposite angles equal Sum of angles = 360 ° 5 sides Regular polygon 6 sides Can be regular polygon 8 sides Can be regular polygon 10 sides Can be regular polygon Where do we see Regular Polygons in real Life? Proof Convex or Concave? A Polygon is a plane figure formed by three or more segments. A Polygon can either be convex or concave. If a polygon is convex then no sides go through the interior of the polygon. (All vertices point outside the polygon.) If a polygon is concave then it is not convex. A side goes through the interior of the polygon. (At least one vertex points inside the polygon.) Example 1: Which figures are polygons? Example 1: Which figures are polygons? polygon polygon polygon polygon Example 2: Label the polygons as convex or concave? Example 2: Label the polygons as convex or concave? convex concave concave convex Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Sides Interior Angles Perimeter Exterior Angles Area Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Interior Angles Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Interior Angles Exterior Angles Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Sides Interior Angles Exterior Angles Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Sides Interior Angles Perimeter Add all sides Exterior Angles Parts of a polygon The simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean. Vertices Sides Interior Angles Perimeter Exterior Angles Area Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Consecutive Diagonal Regular Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Consecutive Diagonal Refers to parts that are right next to each other. (They share a common vertex or side.) Regular Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Consecutive Diagonal Joins two nonconsecutive vertices. (Notice the triangle does NOT have any diagonals.) Regular Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Consecutive Diagonal A polygon that is equilateral and equiangular. Regular Classifying Polygons A Polygon is classified by its’ number of sides. Number of Sides 3 4 5 6 7 8 9 10 12 n Type of Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n - gon (click here for more)
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