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Geometry 6-1 Properties of Polygons • Polygon: multi-sided shaped. – Traits: straight lines, lines don’t cross, closed Polygons Not Polygons Parts of a Polygon Diagonal: segment that connects two nonconsecutive vertices Names of Polygons Definitions • Convex: all diagonals are inside the shape. • Concave: at least one diagonal goes outside the shape. • Regular polygon: a polygon that is convex, equilateral, and equiangular • A polygon that is not regular is irregular Tell whether the follow polygons are regular/irregular and concave/convex. irregular, convex regular, convex irregular, concave regular, convex Geometry 6-1 Interior and Exterior Angles of Polygons • Draw the following shapes: – Triangle – Rectangle (Quadrilateral) – Pentagon – Hexagon – Octagon • Draw all possible diagonals from one of the vertices. Table n (# of sides) 3 4 5 6 7 8 n # of Triangles Sum of Interior Angles Table n (# of sides) # of Triangles Sum of Interior Angles 3 4 5 6 7 1 2 3 4 5 180° 360° 540° 720° 900° 8 n 6 (n - 2) 1080° (n – 2) x 180° Example • Find the sum of each interior angle of a regular 25-gon. (25 – 2) x 180 = 4140° for all 25 angles 4140° / 25 = 165.6° for each angle Measure of Exterior Angles The sum of the exterior angles of a convex polygon is always 360°. Example: Find the measure of each exterior angle of a regular hexagon. 360° / 6 = 60° for each exterior angle

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