Created by: Cathy and Jim Carroll

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, when extended, pass through the interior of the polygon. (All vertices point outside the polygon.) A polygon is concave when a side that is extended passes 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

Example 3: Identifying and Classifying Regular Polygons Name each polygon and tell whether it is a regular polygon. If it is not, explain why not. The figure is a regular quadrilateral. A regular quadrilateral is also called a square. The figure is a quadrilateral. It is not a regular polygon because all of the sides are not congruent. A. B. Course 2

Now You Try… Insert Lesson Title Here The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent. The figure is a regular triangle. Name each polygon and tell whether it is a regular polygon. If it is not, explain why not. A. B. Course 2

Is the figure convex or concave? A.Convex B.Concave

Is the figure convex or concave? A.Convex B.Concave

Is the figure convex or concave? A.Convex B.Concave

Decide whether the figure is equilateral, equiangular, or neither. A. Equilateral B.Equiangular C.Neither

Decide whether the figure is equilateral, equiangular, or neither. A. Equilateral B.Equiangular C.Neither

Decide whether the figure is equilateral, equiangular, or neither. A. Equilateral B.Equiangular C.Neither

True or False The figure is regular. TRUE

True or False The figure is regular. FALSE

True or False The figure is regular. TRUE

The below figure is regular. Find the value of x. x = 5

The below figure is regular. Find the value of x. x = 36

The below figure is regular. Find the value of x. x = 7