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Download Chapter 6 Notes Section 6.1 Polygons Definitions
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Transcript
Chapter 6 Notes Section 6.1 Polygons Definitions Polygon Is formed by three or more segments called sides, such that no two sides with a common endpoints are collinear. Each side intersects exactly two other sides, one at each endpoint. Vertex The endpoints of a side of a polygon Diagonal A segment connecting two nonconsecutive vertices. Convex polygon A polygon that has no line that contains a side of the polygon in the interior of the polygon. Concave polygon A polygon that is not convex. Equilateral polygon A polygon with all sides congruent. Equiangular polygon A polygon with all angles congruent. Regular polygon A polygon that is both equiangular and equilateral. Sides Polygons are named by the number of ________ that they have. # of sides Type of polygon # of sides Type of polygon # of sides Type of polygon 3 Triangle ____________ 4 Quadralateral ____________ 5 Pentagon ____________ 6 Hexagon ____________ 7 Heptagon ____________ 8 Octagon ____________ 9 Nonagon ____________ 10 Decagon ____________ 12 Dodecagon ____________ n nagon ____________ 1 Determin if the following figures are polygons and if it is clasify as concave or convex and by the number of sides. 1. 3. 2. 4. Y or N_______________ Y or N_______________ _______________ 5. _______________ Y or N_______________ _______________ 6. Y or N_______________ _______________ 7. Y or N_______________ Y or N_______________ Y or N_______________ _______________ _______________ _______________ Draw a diagonal in the above quadrilateral. You divide it into two __________, each of which has interior angles that add up to _________ degrees. What can you conclude about the sum of the interior angles of a quadrilateral? 2 Theorem 6.1 Interior Angles of a Quadrilateral The sum of the measure of the interior angles of a quadrilateral is 360 . 2 3 m 1 + m 2 + m 3 + 4 = 360 1 4 Use the given information to solve for x. 2. 1. 98 2x + 25 113 3. 5x 30 3x + 5 x 8x + 8 42 10x +12 6x7 Draw a figure that fits the following description. 1. A concave octagon Homework: 2. A convex decagon Page; 325 3. An equilateral hexagon that is not regular. Problems; 146 3 4
