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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
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Parts of a Polygon Diagonal: segment that connects two nonconsecutive vertices
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Names of Polygons
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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
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Tell whether the follow polygons are regular/irregular and concave/convex.
irregular, convex regular, convex
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irregular, concave regular, convex
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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.
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Table n (# of sides) # of Triangles Sum of Interior Angles 3 4 5 6 7 8
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Table n (# of sides) # of Triangles Sum of Interior Angles 3 1 180° 4
2 360° 5 540° 6 720° 7 900° 8 1080° n (n - 2) (n – 2) x 180°
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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
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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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