November 11, Polygons. poly means "many" gon means "angles" polygon means "many angles"

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1 3.5 Polygons poly means "many" gon means "angles" polygon means "many angles" note that each polygon is formed by coplanar segments (called sides) such that: each segment intersects exactly 2 other segments, 1 at each endpoint no 2 segments with a common endpoint are collinear are these all polygons? Why are these not polygons? How are these two groups of polygons different? onvex polygons In our class our book, when we say polygon we mean convex polygons Non convex (concave) polygons

2 onvex polygons In our class our book, when we say polygon we mean convex polygons It is a polygon such that: no line containing a side of the polygon contains a point in the interior of the polygon We classify polygons by the number of sides... 3 triangle 4 quadrilateral 5 pentagon 6 hexagon 8 octagon 10 decagon n n-gon (or n-agon) WHN NMING POLYGON, YOU MUST NM TH VRTIS IN ORR!!!! iagonal is a segment that joins two non consecutive vertices THM: The sum of the measures of the angles of a convex polygon with n sides is (n-2) sides 2 triangles angle sum = 2(180) number of sides = 4 angle sum = (4-2)(180) 5 sides 3 triangles angle sum = 3(180) number of sides = 5 angle sum = (5-2)(180) 6 sides 4 triangles angle sum = 4(180) number of sides = 6 angle sum = (6-2)(180) now we'll do the triangle exterior angles activity

3 THM: The sum of the measures of the exterior angles of any convex polygon, one angle at each angle, is. polygon has 32 sides. Find (a) the sum of the measures of the interior angles (b) the sum of the measures of the exterior angles, one at each vertexes (a) interior angles sum (32-2) (b) exterior sum hexagon that is neither equiangular or equilateral. hexagon that is equiangular If a polygon is both equiangular or equilateral, it is called a regular polygon. hexagon that is equilateral hexagon that is both equiangular equilateral, thus regular.

4 regular polygon has 12 sides. Find the measure of each interior angle. regular polygon has 12 sides. Find the measure of each exterior angle. interior angles sum (12-2) each of 12 congruent angles 1800/ exterior angles sum each of 12 congruent exterior angles /12 30 each of 12 congruent interior angles Find (a) the sum of the measures of the interior angles, (b) the sum of the measures of the exterior angles, one angle at each vertex. For a polygon with 7 sides. Find (a) the sum of the measures of the interior angles, (b) the sum of the measures of the exterior angles, one angle at each vertex. For a 17-gon for a regular quadrilateral for a regular octagon

5 for a regular polygon with 15 sides for a regular polygon with 20 sides always sometimes The sum of the measures of the exterior angles of any polygon, one angle at each vertex, is. The sum of the measures of the angles of a convex polygon is. sometimes never segment joining two vertices of a polygon is a diagonal. The sum of the measures of the exterior angles of any polygon depends on the number of sides of the polygon.

6 always sometimes regular polygon is equilateral. n equiangular polygon is regular Find the interior angle sum the exterior angle sum for: a triangle Find the interior angle sum the exterior angle sum for: a 20-gon Find the interior angle sum the exterior angle sum for: a 27-gon omplete. The exterior angle of a regular polygon has measure 10. The polygon has sides.

7 18 95 omplete. The interior angle of a regular polygon has measure 160. The polygon has sides. omplete. Three of the angles of a quadrilateral have measures 90, 60, 115. The fourth angle has measure.

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