Geometry Chapter 6-1

1. Geometry Chapter 6-1 By: Jordan Harrison, Stephen Gardner, Rachel Kibby, Anthony Thomson, & Lora Laherty

2. Classifying a Polygon  concave Regular Polygon- When a polygon’s sides are all congruent and angles are all congruent Irregular Polygon- When not all the sides or angles of a polygon are congruent Concave Polygon- When you can draw a line from one vertex of a polygon to another and the line is not always in the interior of the polygon Convex Polygon- When you draw a line from one vertex of a polygon to another and the line is always in the interior  convex  regular  irregular

3. Number of Sides & Exterior Angle Measure Number of Sides Polygons are named by the number of sides they have. Refer to the Table to the right for the names of polygons. Exterior Angle Measures The sum of the exterior angle measures of any polygon always equals 360 ̊

4. Interior Angle Measure Sum Step 1:Count sides. There are 4 To find the sum of the interior angle measures of a polygon, you must use this equation: (n-2)180 You plug in the number of sides on the polygon for n. Then solve. Insert 4 for n. (4-2)180 Solve. 2(180) 360 There are 360 ̊ in the polygon.

5. Find the measure of angle b in the quadrilateral Finding the measure of a single interior angle  angle b To find the measure of a single interior angle, first you follow the steps in the last slide to find the sum of the interior angle measures. You then simply add up all of the variables and their coefficients and divide the sum of the interior angle measures by the coefficient. (solve for the variable) then plug the variable into the equation of the angle that you are trying to find the measure of….  Count number of sides. There are 4. plug into the equation. (4-2)180=360 Count the variables and coefficients. Set up the equation: 8c=360 Solve for c C=45 Plug in 45 for c and solve Angle b=3c Angle b=3(45) Angle b=135 ̊

6. Solving for Exterior Angle Measures Problem: Find the measure of angle b 1. Add variables 3c+4c+5c=12c To solve for a single angle measure you add up the variables as you did in the previous slide. Then write the equation as: Xc=360 X is the coefficient you count up when counting the variables. Simply divide 360 by the coefficient in front of c and then plug in c into the equation of any exterior angle measure. Set up equation: 12c=360 Angle b  Solve for c Finally, solve for c C=30 Lastly, plug c into the equation of the angle measure you are trying to find… Angle b=3c Angle b=3(30) Angle b=90˚

7. Theorems and Postulates! • Theorem 6-1-1 (polygon angle sum theorem) The sum of the interior angle measures of a convex polygon with n sides is: (n - 2)180˚. • Theorem 6-1-2 (polygon exterior angle sum theorem) The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360˚.

8. Vocabulary! • Side of a polygon- one of the segments that forms a polygon • Vertex of a polygon-the intersection of two sides of the polygon • Diagonal of a polygon- a segment connecting two nonconsecutive vertices of a polygon • Regular polygon- a polygon in which all the sides and angles are equal to each other • Concave polygon-a polygon in which a diagonal can be drawn such that the part of the diagonal contains points in the exterior of the polygon • Convex polygon- a polygon in which no diagonal contains points in the exterior of the polygon

9. Credits By: Jordan Harrison Rachel Kibby Lora Laherty Anthony Thomson Stephen Gardner With the help of: Mrs. Geshwender Holt Geometry. New York: Holt Rinehart & Winston, 2004. Print.

10. THE END!