+ Polygon Angle Sum Theorem (3.4) Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons.

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Presentation transcript:

+ Polygon Angle Sum Theorem (3.4) Objective: To classify polygons, and to find the sums of interior and exterior angles of polygons

+ Polygon Closed plane figure At least 3 sides that are segments Sides intersect only at endpoints Adjacent sides are NOT collinear POLYGONSNOT POLYGONS

+ To Name a Polygon… 1. Start at any vertex 2. List vertices consecutively Example: Name the polygon. Name the sides and angles. Name ____________________________ Sides _____________________________ Angles ____________________________

+ Common Polygons SIDESNAME 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon

+ Concave vs. Convex CONCAVE PolygonCONVEX Polygon At least one diagonal outside polygon Has an indent in at least one edge (“caves in”) No diagonal with points outside polygon Has no indents in any edges

+ Polygon-Angle Sum Theorem The sum of the measures of angles in an n-gon: Example: Find the sum of the measures of a 15-gon.

+ Finding missing angle measures 1. Figure out what the sum of the interior angles should be 2. Add up expressions and set them equal to the sum from part one. Example #1:

+ Examples #2. The sum of the measures of a given polygon is 720. How many sides are in the polygon? #3 Pentagon ABCDE has 5 congruent angles. Find the measure of each angle.

+ Polygon-Exterior Angle Sum Theorem The sum of the measures of exterior angles of a polygon is ALWAYS YouTube Video Example #4: What is the sum of the exterior angles for a 500-gon?

+ EQUILATERAL POLYGON: All sides congruent EQUIANGULAR POLYGON: All angles congruent REGULAR POLYGON: Equilateral AND Equiangular ONE Interior Measure ONE Exterior Measure

+ More Examples… #5. The sum of the measures of angles of a polygon with n sides is Find n, the number of sides. #6. Find the measures of one interior angle and one exterior angle of a REGULAR hexagon.

+ Last One! #7. The measure of an exterior angle of a regular polygon is 30. What is the measure of an interior angle? How many sides are there?