6 1 Properties and Attributes of Polygons Classify
6 -1 Properties and Attributes of Polygons Classify polygons based on their sides and angles. 6. 1 Find and use the measures of interior and exterior angles of polygons. Holt Geometry Side of a polygon Vertex of a polygon Diagonal Regular polygon Concave convex Polygon Angle Sum Theorem Polygon Exterior Angle Sum Theorem
Number your paper 1. 2. 3. 4. 5. 6.
6 -1 Properties and Attributes of Polygons Classifying polygons by number of sides. Holt Geometry
6 -1 Properties and Attributes of Polygons A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. regular Holt Geometry irregular Concave: any diagonal passes outside of the polygon Convex: no diagonal passes outside the polygon
Number your paper 1. 2. 3. 4. 5.
6 -1 Properties and Attributes of Polygons Tell whether each polygon is regular or irregular and concave or convex. Holt Geometry
1. Draw these! 2. 4. 3. 5.
6 -1 Properties and Attributes of Polygons Examples: Sketch a polygon that meets each of the following characteristics, if possible. 1. convex, irregular hexagon 2. concave triangle. 3. Regular quadrilateral 4. convex nonagon 5. concave, regular pentagon Holt Geometry
6 -1 Properties and Attributes of Polygons Find the sum of the interior angle measures of each convex polygon by drawing all possible diagonals from one vertex of the polygon. How does the triangle sum theorem help you? Holt Geometry
6 -1 Properties and Attributes of Polygons Holt Geometry
6 -1 Properties and Attributes of Polygons Example 1: Find the sum of the interior angle measures of a convex heptagon. Holt Geometry
6 -1 Properties and Attributes of Polygons Example 2: Find the measure of each interior angle of pentagon ABCDE. Holt Geometry
6 -1 Properties and Attributes of Polygons How would you calculate the measure of each interior angle of a regular decagon? What if it’s not regular? Holt Geometry
Interior Angles Sum of all angles Measure of one if the polygon is REGULAR! Exterior Angles
6 -1 Properties and Attributes of Polygons What is the measure of each interior angle of a regular decagon? What is the measure of each exterior angle of a regular decagon? What is the SUM of all of the exterior angles? Holt Geometry
6 -1 Properties and Attributes of Polygons In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°. Holt Geometry
Angle measures of a convex polygon with n sides Interior Angles Sum of all angles Measure of one if the polygon is REGULAR! Exterior Angles
6 -1 Properties and Attributes of Polygons Example 3: Find the value of b in polygon FGHJKL. Holt Geometry
6 -1 Properties and Attributes of Polygons Example 4 Find the measure of each exterior angle of a regular 20 -gon. Holt Geometry
6 -1 Properties and Attributes of Polygons Ann is making paper stars for party decorations. If the pentagon in the center of the star is regular, what is the measure of 1? 2 Holt Geometry
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