POLYGONS! gone! Polly

What is a polygon? The term POLYGON means "many-angled" (Poly = many) & (Gon = angles)  By definition A Polygon is: a closed figure formed by a finite number of coplanar segments such that the sides that have a common endpoint are noncollinear and each side intersects exactly two other sides, but only at their endpoints                               Wow that is pretty technical...... does that make sense to you?.... basically a polygon is a closed shape that is made up of line segments (no curves) and of course sides can only touch at the endpoints......                        Does that make more sense?   POLYGONS Non Polygons

Polygons are classified according to the number of sides they have. A polygon is a closed plane figure bounded by straight line segments. The line segments are called the sides of the polygon, and the points at which they intersect are called vertices. A polygon has the same number of sides as it has vertices. Polygons are classified according to the number of sides they have. What is a three-sided polygon called? What is a four-sided polygon called?

Other polygons Name these other polygons.

Click here to see some more polygon names

Name the polygons.

What kinds of polygons do you see?

Math is everywhere! Name the polygons that you see.

polygon art: polygons?

What kind of triangle is regular? If all the sides and all the angles of a polygon are congruent the polygon is said to be regular. What kind of triangle is regular? What kind of quadrilateral is regular? Equilateral triangle square pentagon hexagon octagon decagon heptagon nonagon

A polygon that is not regular is irregular.

Concave and Convex polygons A concave polygon is 'caved' in - some of its sides are bent inward.  For example the red and green shape are both concave polygons.  An easy way to determine whether a shape is concave or not is the SEGMENT TEST.  If you can draw a straight segment between two points in the shape but part of the segment leaves the shape then the shape is concave.   A convex polygon is the opposite of concave - when the segment test fails for all segments in the shape.  A more formal way of defining convex is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. concave convex

Convex or Concave? 1. convex 2. concave 4. 3. 5. 6.

take a quick polygon quiz. Test yourself! Click on the button to take a quick polygon quiz. QUIZ

diagonals A diagonal is a segment drawn from one vertex to another that is not a side. Some diagonals: All of the diagonals in a convex polygon will lie inside the polygon. At least one diagonal in a concave polygon will lie outside of the polygon.

Interior Angles The interior angles in a polygon are formed by the sides. Interior angle The number of interior angles is equal to the number of sides and number of vertices in the polygon.

What is the sum of the measures of the interior angles in in a triangle is ____________. in a convex quadrilateral is _____________. What is the sum of the measures of the interior angles in any convex polygon?

Make a table to look for a pattern. Polygon name Number of sides # of diagonals drawn from one vertex # of triangles formed Sum of measures of interior angles triangle quadrilateral 5 6 7 8 9 n 3 1 180 360 4 1 2 pentagon 2 540 3 180 180 180 180 180

Formula for finding the sum of the measures of the interior angles in a convex polygon: (n - 2) 180 n = number of sides

Exterior angles Exterior angles are formed by extending a side of the polygon. exterior angle exterior angle exterior angle exterior angle

exterior angles of a polygon? What is the sum of the exterior angles of a polygon? (that means one exterior angle at each vertex) 360° Sum of exterior angles = 120° 60° TRIANGLE 120° 60° 60° 120°

360° 360° 110° 120° 120° 95° 95° Sum of exterior angles = QUADRILATERAL PENTAGON 360° Sum of exterior angles =

angles of any convex polygon (one angle at each vertex) is . . . The sum of the exterior angles of any convex polygon (one angle at each vertex) is . . . 360°

take a quick polygon quiz. Test yourself! Click on the button to take a quick polygon quiz. QUIZ

Helpful polygon websites: Definitions / examples Polygon definition Regular / irregular Click on the button to go to a website. “textbook” Geometry home page Venn diagrams