Lesson Plan #39 Class: Geometry Date: Tuesday December 11 th, 2018 Topic: Sum of the measures of the interior angles of a polygon Objectives: Aim: What is the sum of the measures of the interior angles of a polygon? 1) Students will be able find the sum of the measures of the interior angles of a triangle. 2) Students will be able to find the sum of the measures of the exterior angles of a triangle. HW #39: Page 104 # s 1-6, 8, 9, 10, 11 Do Now: Procedure: Write the Aim and Do Now Get students working! Take attendance Give Back HW Collect HW Notice each of the interior angles of the polygons at right measures less than 180 o. These are known as convex polygons. If the polygon has at least one angle measuring more than 180 o, it is called a concave polygon. Question:What do we call a polygon whose sides are all the same length and whose angles are all the same measure? Online Interactive Activity: Let s see regular polygons in action. Let s go to http://www.mathopenref.com/polygonregular.html We proved that the sum of the measures of the angles of a triangle is 180 o and the sum of the measures of the angles of a quadrilateral is 360 o. Let s see how we can find the sum of the angles of a pentagon, then try to generalize a formula for the sum of the interior angles of a polygon of n sides. Examine the pentagon at the right. To help you discover the formula, see how many non-overlapping triangles you can create, then use this to come up with a sum of the angles of a pentagon.
Try it for a six sided figure (hexagon). What is the formula for the sum of the interior angles of a polygon with n sides? Proof: http://www.qc.edu.hk/math/junior%20secondary/interior%20angle.htm Online Interactive Activity: Let s check out the sum of the interior angles of a polygon in action. Let s go to http://www.mathopenref.com/polygoninteriorangles.html Online Interactive Activity: Let s check out the sum of the exterior angles of a polygon, taking one exterior angle at each vertex.http://www.qc.edu.hk/math/junior%20secondary/interior%20angle.htm http://www.mathopenref.com/polygonexteriorangles.html What is the formula for the sum of the exterior angles of any polygon of n sides, taking one exterior angle at each vertex? Sample Test Questions: Group Work 1) 2) What is the sum of the interior angles of a regular dodecagon (12-sided polygon)? 3) Each of the interior angles of a regular polygon is 156. How many sides does the polygon have? 4) 5) 6) 7)
8) 9) 10) 11) 12) H.O.T. Question #1: 1) The sum of the degrees measures of the interior angles of a polygon of n sides is equal to 3x 3and the number of sides is equal to x 176. A) Find x B) Find the number of sides in the polygon C) Find the sum of the degree measures of the interior angles. H.O.T. Question #2: 2) In a regular polygon, the measure of each interior angle is 21.6 more than 10 times the measure of its exterior angle. A) Find the number of sides in the regular polygon B) Find the measure of each interior angle. C) Find the measure of each exterior angle. D) Find the sum of the measures of the interior angles. E) Find the sum of the measures of the exterior angles. F) How many distinct diagonals does this polygon have.
More H.O.T Questions 1) In the diagram at the right with ACD where BC and EC Intersect at C. C is the midpoint of AD and m 90 o ABC m DEC. 1 2. Evaluate y x if x 10 2) Evaluate x y Assignment: Complete the exercises below in your groups
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