2 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 thatthe sides that have a common endpoint are noncollinear andeach 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? POLYGONSNon Polygons
3 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?
10 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?Equilateraltrianglesquarepentagonhexagonoctagondecagonheptagonnonagon
12 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.concaveconvex
14 take a quick polygon quiz. Test yourself!Click on the button totake a quick polygon quiz.QUIZ
15 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 lieinside the polygon.At least one diagonal in a concave polygon will lie outside of the polygon.
16 Interior Angles The interior angles in a polygon are formed by the sides.Interior angleThe number of interior angles is equal to the number of sides and numberof vertices in the polygon.
17 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 measuresof the interior angles inany convex polygon?
18 Make a table to look for a pattern. PolygonnameNumber of sides# of diagonals drawn from one vertex# of triangles formedSum of measures of interior anglestrianglequadrilateral56789n31180360412pentagon25403180180180180180
19 Formula for finding the sum of the measures of the interior angles in a convex polygon:(n - 2) 180n = number of sides
20 Exterior angles Exterior angles are formed by extending a side of the polygon.exterior angleexterior angleexterior angleexterior angle
21 exterior angles of a polygon? What is the sum of theexterior angles of a polygon?(that means one exterior angle at each vertex)360°Sum of exterior angles =120°60°TRIANGLE120°60°60°120°
22 360° 360° 110° 120° 120° 95° 95° Sum of exterior angles = QUADRILATERALPENTAGON360°Sum of exterior angles =
23 angles of any convex polygon (one angle at each vertex) is . . . The sum of the exteriorangles of any convex polygon(one angle at each vertex) is . . .360°
24 take a quick polygon quiz. Test yourself!Click on the button totake a quick polygon quiz.QUIZ
25 Helpful polygon websites: Definitions / examplesPolygon definitionRegular / irregularClick on the buttonto go to a website.“textbook”Geometry home pageVenn diagrams