Presentation on theme: "Sec. 3-5 The Polygon Angle-Sum Theorems"— Presentation transcript:
1Sec. 3-5 The Polygon Angle-Sum Theorems Objectives:To classify PolygonsTo find the sums of the measures of the interior & exterior s of Polygons.
2Polygon: A closed plane figure. w/ at least 3 sides (segments) The sides only intersect at their endpointsName it by starting at a vertex & go around the figure clockwise or counterclockwise listing each vertex you come across.
3Which of the following figures are polygons? NoyesNo
4Example 1: Name the 3 polygons TopXSTUSTBottomWVUXXUBigSTUVWXVW
5I. Classify Polygons by the number of sides it has. 34567891012nNameTriangleQuadrilateralPentagonHexagonHeptagonOctagonNonagonDecagonDodecagonN-gonInterior Sum
6II. Also classify polygons by their Shape a) Convex Polygon – Has no diagonal w/ points outside the polygon.EADBCb) Concave Polygon – Has at least one diagonal w/ points outside the polygon.* All polygons are convex unless stated otherwise.
12Th(3-10) Polygon Exterior -Sum Thm The sum of the measures of the exterior s of a polygon is 360°.Only one exterior per vertex.123m1 + m2 + m3 + m4 + m5 = 36054For Regular PolygonsThe interior & the exterior are Supplementary.= measure of one exterior Int + Ext = 180
13Example 4:How many sides does a polygon have if it has an exterior measure of 36°.= 36360 = 36n10 = n
14Example 5: S = (n - 2)180 = (15 – 2)180 = 24 = (13)180 = 2340 n = 15 Find the sum of the interior s of a polygon if it has one exterior measure of 24.S = (n - 2)180= (15 – 2)180= (13)180= 2340= 24n = 15
15Example 6: Solve for x in the following example. 4 sides Total sum of interior s = 360100x = 360280 + x = 360x = 80
16Example 7:Find the measure of one interior of a regular hexagon.S = (n – 2)180= (6 – 2)180= (4)180= 720= 120