1. Geometry Ch.6 6.1 Classify Polygons

2. Identifying Polygons In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. It is formed by three or more line segments called sides. Each side intersects exactly two sides, one at each endpoint, so that no two sides with a common endpoint are collinear.

3. Each endpoint of a side is a vertex of the polygon. The plural of vertex is vertices. A polygon can be named by listing the vertices in consecutive order. The polygon shown here has six vertices. It is a hexagon.

4. A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is called nonconvex or concave. ConvexConcave

5. Classifying Polygons: A polygon is named by the number of its sides 3triangle 4quadrilateral 5 pentagon 6hexagon 7heptagon 8octagon 9nonagon 10decagon 12dodecagon nn-gon The term n-gon, where n is the number of a polygon’s sides, can also be used to name a polygon. For example, a polygon with 14 sides is a 14-gon.

6. In an equilateral polygon, all sides are congruent. In an equiangular polygon, all angles in the interior of the polygon are congruent. A regular polygon is a convex polygon that is both equilateral and equiangular. Regular polygons are shown to the right.

7. Ex.1 Practice—any volunteers to sketch an example of a convex hexagon and a concave hexagon?

8. Ex.2: Extra practice: Using properties, tell whether the statement is always, sometimes, or never true. A triangle is convex A decagon is regular A regular polygon is equiangular A circle is a polygon A polygon is a plane figure A concave polygon is regular

9. Ex. 3. Let x be the length in inches. If a figure is a regular decagon, and the length of one side is 2x + 8 and the length of another side is 4x + 4, find the length of each side of this regular decagon.

10. Ex. 3. Let x be the length in inches. If a figure is a regular decagon, and the length of one side is 2x + 8 and the length of another side is 4x + 4, find the length of each side of this regular decagon. 2x + 8 = 4x + 4 2 x =4x – 4 -2 x = – 4 x = 2 2(2) + 8=12 The length of each side is 12 inches

11. Theorem 6.1 Interior Angles of a Quadrilateral The measure of the interior angles of a quadrilateral is 360 degrees.

12. Websites used in preparation for this PPT: www.seal-pa.org www.mathleague.com http://www.pinkmonkey.com/studyguides/subjects/geometry/chap1/Image434.gif http://math247.pbwiki.com/f/6mg2.2.gif http://www.google.com/imgres?imgurl=http://education.yahoo.com/homework _help/math_help/solutionimages/miniprealggt/7/1/1/miniprealggt_7_1_1_ 7_70/f-452-3-pr- q.gif&imgrefurl=http://education.yahoo.com/homework_help/math_help/pr oblem%3Fid%3Dminiprealggt_7_1_1_7_70&h=300&w=300&sz=1&tbnid= gdnCOqLtam8J::&tbnh=116&tbnw=116&prev=/images%3Fq%3Dvertical %2Bangles&sa=X&oi=image_result&resnum=3&ct=image&cd=1 http://images.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedi a/commons/thumb/8/8f/Simple_polygon.svg/588px- Simple_polygon.svg.png&imgrefurl=http://commons.wikimedia.org/wiki/Im age:Simple_polygon.svg&h=521&w=588&sz=14&hl=en&start=16&um=1& tbnid=chzcOy4W_qR_lM:&tbnh=120&tbnw=135&prev=/images%3Fq%3D polygon%26um%3D1%26hl%3Den%26client%3Dfirefox- a%26rls%3Dorg.mozilla:en-US:official%26sa%3DG http://mathforum.org/sum95/math_and/poly/reg_polygons.gif