Transcript Whiteboard
Happy Monday! • Take out your worksheet from Friday • Take out your whiteboard marker and whiteboard • Take out a piece of paper and title it – 6.1: Angles of Polygons • Pick up the paper from the front table Homework: p 386 #1-15, 23-33 odd 3 Things Lets’ Warm-Up! 1) Sketch a polygon on your whiteboard. Compare with someone Horizontal to you. Do you agree it’s a polygon? 2) Sketch a non-example of a polygon on your whiteboard. Compare with someone Vertical to you. Do you agree it is not a polygon? Lets’ Warm-Up! 3) With the person vertical to you discuss the difference between a concave and convex polygon. Sketch a concave and convex polygon on your whiteboard. 4) With the person horizontal to you, discuss the difference between a regular and irregular polygon. Sketch a regular and irregular polygon on your whiteboard. Whiteboard 1. Tell whether the figure is a polygon. If it is a polygon do the following: o name it by the number of sides o Decide whether it is regular or irregular o Decide whether it is concave or convex (a) (d) 6.1: Angles of Polygons • Learning Objective – SWBAT find and use the measures of interior and exterior angles of polygons Vertex • Common endpoint of two sides. Diagonal • A segment that connects any two nonconsecutive vertices. Whiteboards • How many degrees do a triangle add up to? Interior Angles of a Convex Polygon 1. Draw a convex polygon. 2. Draw all possible diagonals from one vertex of the polygon 3. How many triangles did you create? 1. How many degrees do you think the interior angles of your polygon add up to? Ex) 6-1 Properties and Attributes of Polygons Deriving the Polygon Angle Sum Theorem Polygon Triangle Quadrilateral Pentagon Hexagon n-gon Number of Sides Number of Triangles that can create the polygon Sum of Interior Angle Measures of the polygon Formula.. • Talk with your partner… Can you come up with a formula to determine the sum of the interior angles measures of a convex polygon with n sides? Polygon Angle Sum Theorem Example 1: Finding the Interior Angle Measures and Sums in Polygons Find the sum of the interior angle measures of a convex heptagon. Whiteboards Find the measure of each interior angle of a regular 16-gon. Whiteboards • Find the measure of <C Exterior Angles Whiteboards: Looking at the same figure from the last problem, draw one exterior angle on the polygon. If I am to continue drawing exterior angles for every side of my polygon, I must continue in the same direction. For example if I began clockwise, I must continue clockwise. Exterior Angles Exterior Angle • An exterior angle is formed by one side of a polygon and the extension of a consecutive side 6-1 Properties and Attributes of Polygons Exploring Polygon Exterior Angle Sum Theorem On the back of your worksheet, attempt to use the two examples of polygons with exterior angles to understand what the sum of all exteriors angles of any polygon will be. http://www.mathopenref.com/polygonexteriorangles.html Polygon Exterior Angle Sum Theorem o The Sum of exterior angle measures of a convex polygon is 360°. Exterior Angles Here are polygons with their exterior angles. What do they both have in common? Exterior Angles • The sum of the exterior angle measures (one angle at each vertex) of a convex polygon is 360° • OR • 360/ n= each exterior angle Example 2: Finding Exterior Angle Measures in Polygons Find the measure of each exterior angle of a regular 20-gon. Whiteboards Find the value of b in polygon FGHJKL. Whiteboards • Find the measure of each exterior angle of a regular dodecagon. Example 3: Application Ann is making paper stars for party decorations. What is the measure of 1? Whiteboards The aperture of the camera is formed by 8 blades. What would the measure of each exterior angle be? What if…? It was 10 blades instead of 8? Exit Ticket 1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex. 1. Find the sum of the interior angle measures of a convex 11-gon. 2. Find the measure of each interior angle of a regular 18-gon. 3. Find the measure of each exterior angle of a regular 15-gon Think – Write - Share Answer the following question on your worksheet under Todays Summary. How would you summarize todays lesson for someone who wasn’t here?