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Published byBrian Brent Hubbard Modified over 4 years ago

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**Honors Geometry Sections 3.1 & 3.6 Polygons and Their Angle Measures**

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**The word polygon means many sides**

The word polygon means many sides. In simple terms, a polygon is a many-sided closed figure.

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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

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

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

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

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

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**Polygons are classified according to the number of its sides**

Polygons are classified according to the number of its sides ____________ ____________ 5 - ____________ ____________ 7 - ____________ ____________ 9 - ____________ ___________ 12 - ___________ n - ___________ triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n - gon

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

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

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

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**Corollary to Theorem 3.6.1 The measure of each interior angle of a regular n-gon is**

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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.

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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.

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

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**Here’s an example of why that is the case**

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

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**Corollary to Theorem 3.6.3 The measure of each exterior angle of a regular n-gon is**

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**Complete this table for regular polygons. **

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**Complete this table for regular polygons. **

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