Download Topic: Sum of the measures of the interior angles of a polygon

Lesson Plan #39
Class: Geometry
Topic: Sum of the measures of the interior angles of a polygon
Date: Friday December 9th, 2016
Aim: What is the sum of the measures of the
interior angles of a polygon?
Objectives:
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
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Notice each of the interior angles of the polygons at right measures less than
180o. These are known as convex polygons.
If the polygon has at least one angle measuring more than 180o, 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 180o and the sum of the measures
of the angles of a quadrilateral is 360o. 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 below. 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:
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?
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Assignment: Complete the exercises below