3.4 Exploring Polygons Thompson Exploring Convex and Concave Polygons Parts of a Polygon Classifying Polygons W/ some triangle review

 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 Polygons in real Life?

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

Example 2: Label the polygons as convex or concave?

Example 2: Label the polygons as convex or concave? convexconcave 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. VerticesInterior AnglesExterior Angles Perimeter Area Sides

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. VerticesInterior 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. VerticesInterior AnglesExterior 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. VerticesInterior AnglesExterior Angles Sides

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. VerticesInterior AnglesExterior Angles Perimeter Add all sides Sides

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. VerticesInterior AnglesExterior Angles Perimeter Area Sides

Parts of a polygon In more complex polygons there are more parts. Learn these new terms: DiagonalRegularConsecutive

Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Refers to parts that are right next to each other. (They share a common vertex or side.) DiagonalRegularConsecutive

Parts of a polygon In more complex polygons there are more parts. Learn these new terms: DiagonalRegularConsecutive Joins two nonconsecutive vertices. (Notice the triangle does NOT have any diagonals.)

Parts of a polygon In more complex polygons there are more parts. Learn these new terms: A polygon that is equilateral and equiangular. DiagonalRegularConsecutive

Classifying Polygons A Polygon is classified by its’ number of sides nn - gon Dodecagon Decagon Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral Triangle Number of SidesType of Polygon