3 Concave and Convex Polygons If a polygon has an indentation (or cave), the polygon is called a concave polygon. Any polygon that does not have an indentation is called a convex polygon.Any two points in the interior of a convex polygon can be connected by a line segment that does not cut or cross a side of the polygon.Concave polygonConvex polygonWe will only be discussing CONCAVE polygons
5 Important Terms A VERTEX is the point of intersection of two sides F A CONSECUTIVE VERTICES are two endpoints of any side.FABCDEA segment whose endpoints are twononconsecutive vertices is called a DIAGONAL.Sides that share a vertex are called CONSECUTIVE SIDES.
24 More important terms Interior Angles Exterior Anglesthe SUM of an interior angle and it’s corresponding exterior angle = 180o
25 Sums of Exterior Angles 123456180180180•3 = 540180Sum of Interior & Exterior Angles =540Sum of Interior Angles =180Sum of Exterior Angles =540- 180=360
26 Sums of Exterior Angles 180180180180•4 = 720180Sum of Interior & Exterior Angles =720Sum of Interior Angles =360Sum of Exterior Angles =720- 360=360
27 Sums of Exterior Angles Sum of Interior & Exterior Angles =180•5 =900Sum of Interior Angles =180•3 =540Sum of Exterior Angles =360900- 540=
28 What conclusion can you come up with regarding the exterior angle sum of a CONVEX n-polygon?? Sum of Interior & Exterior Angles =180nSum of Interior Angles =180(n-2) = 180n - 360Sum of Exterior Angles =180n – (180n – 360)
29 The exterior angle sum of a CONVEX polygon = 360°
30 Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent
31 Interior Angle Measure of a REGULAR polygons 60°90°Equilateral TriangleAngle measure = 60°SquareAngle measure = 90°These are measurement that we generally know at this time,But what about the other regular polygons?How do we calculate the interior angle measure?