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Honors Geometry Sections 3.1 & 3.6 Polygons and Their Angle Measures

Honors Geometry Sections 3.1 & 3.6 Polygons and Their Angle Measures. The word polygon means m any sides . In simple terms, a polygon is a many-sided closed figure.

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Honors Geometry Sections 3.1 & 3.6 Polygons and Their Angle Measures

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  1. Honors Geometry Sections 3.1 & 3.6Polygons and Their Angle Measures

  2. The wordpolygonmeans many sides. In simple terms, a polygon is amany-sided closed figure.

  3. Formally, a polygon is a figure formed from three or more line segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. The segments are called the_____ of the polygon and the common endpoints are called the _______ of the polygon. sides vertices

  4. When naming a polygon, you must list the vertices in order eitherclockwise or counterclockwise. The polygon at the right could be named _______ or _______ BAFEDC ABCDEF

  5. A diagonal of a polygon is a segment joining two nonadjacent vertices.

  6. A polygon is equilateraliffA polygon is equiangulariffA polygon that is both equilateral and equiangular is called a _______ polygon. all its sides are congruent. all its angles are congruent. regular

  7. The center of a regular polygon is the point which is equidistant from each of the vertices.

  8. Polygons are classified according to the number of its sides.3 - ____________ 4 - ____________5 - ____________ 6 - ____________7 - ____________ 8 - ____________9 - ____________ 10 - ___________12 - ___________ n - ___________ triangle quadrilateral hexagon pentagon octagon heptagon nonagon decagon dodecagon n - gon

  9. A polygon is convexiffthe line containing a side does not contain a point in the interior.A polygon that is not convex is concave.

  10. For each figure, draw all the diagonals from one vertex and complete the table.

  11. Theorem 3.6.1 The sum of the measures of the interior angles of a (convex) polygon with n sides is

  12. Corollary to Theorem 3.6.1The measure of each interior angle of a regular n-gonis

  13. Example 1: Find the sum of measures of the interior angles of a dodecagon. Example 2: Find the measure of each interior angle of a regular 20-gon.

  14. While the sum of the interior angles of a polygon changes as the number of sides changes, this is not the case with the sum of the exterior angles.

  15. Theorem 3.6.3The sum of the measures of the exterior angles of a (convex) polygon, one at each vertex, with n sides is

  16. Here’s an example of why that is the case.Adding the five equations together, we get:

  17. Corollary to Theorem 3.6.3The measure of each exterior angle of a regular n-gonis

  18. Complete this table for regular polygons.

  19. Complete this table for regular polygons.

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