Course Guide - USAID Teacher Education Project

Unit 3 Geometry,Week 2, Session 2: Angles in Polygons, 360-degrees around a Point1. What are the important concepts?a) Any polygon can be dissected into triangles in order to determine the sum of thepolygon's interior angles.This continues the discussion of all triangles having a 180° angle sum from the priorsession.In order to calculate the number of degrees in a given polygon, lines are drawn fromone vertex to all the others. These are termed diagonals. The construction of thesediagonals results in a series of triangles inside the polygon.This process is called "triangulating the polygon." Since each of these trianglescontains 180°, the angle sum of the polygon can be calculated by multiplying 180° bythe number of triangles.b) By calculating (and charting) the angle sum of 3- through 8-sided polygons, apattern will emerge. This pattern results in a formula that can be used to find theangle sum for a polygon of any number of sides.This will result in a completed chart that looks something like this:Note: It is crucial that the completed chart not be given to the students beforehand.Because pattern detection is such an important mathematical trait, the goal is that thestudents should not only learn the triangle sum theorem, but, that they should developthis concept. Adequate time should be allotted for students to develop this concept.c) All polygons with the same number of sides have the same interior angle sum.For homework, students cut various quadrilaterals on the diagonal in order to formtwo triangles, each with an angle sum of 180-degrees. From this activity, studentsshould come to a generalization that this applied not only to squares (the regularquadrilateral) but to any quadrilateral.