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Transcript
Geometry - 8.1 Interior Angles Goal: To determine the measures of interior angles of a polygon Part I. A. On each of the polygons identify the interior angles by shading them in. If a polygon has n sides how many interior angles does it have? B. In one triangle, what is the sum of the interior angles?_____________________ Take out the triangles and the polygon from the envelope. Name of polygon:______________________________ Shade the interior angles of the_______________________ (polygon) . Using the triangles create a _________________ (polygon), where each of the vertices, A, of the triangles meet inside the polygon. Sketch the __________________ (polygon) you have created with the triangles. A C. How many triangles were needed to create the _____________________(polygon)? ____________ What is the total sum of the measures of the interior angles of all the triangles you used to create the______________________(polygon)? _______________ Identify and shade the interior angles of the triangles that are NOT interior angles of the ________________(polygon). What is the sum of these angles?_______________________________ Based on the above what is the sum of the measures of the interior angles in the __________________ (polygon)? ____________ Explain why. _____________________________________________________________________________ ________________________________________________________________________________________ Teacher Checkpoint__________ (Need signature before transferring to poster paper.) Part II. Class Results A. Sketch each of the diagrams that the groups present and note their ideas. B. 1. Given the number of sides of a regular polygon, how you can calculate the sum of the measures of the interior angles. _________________________________________________________________________________________ _________________________________________________________________________________________ 2. If you were given the sum of the measures of the interior angles in a regular polygon, how would you find the measure of one angle? __________________________________________________________________________________________ __________________________________________________________________________________________ C. Regular Polygon # of Sides # of Triangles triangle 3 1 Sum of interior angle measures D. So far, you have been able to find the sum of the measures of a regular polygon. Does your method work for any convex polygon? How do you know? E. Write an equation that will give the sum of the measures of the interior angles in a convex polygon, S, if there are n sides: III. Practice with Interior Angles 1. Find the sum of the measures of the interior angles of an 11-gon. 2. Find the measure of one interior angle of a regular dodecagon. o 3. The sum of the measures of the interior angles of a polygon is 2340 . Find the number of sides and classify the polygon by sides.
