Geometry, Teacher\'s Edition

2.6 Quadrilaterals

Interior Angles

All Those Polygons –Although they have probably been taught it before, not all students will remember the names
of the different polygons. There are not very many opportunities in life to use the word heptagon. Add these words
to their vocabulary list.

This is most likely the first time they have been introduced to a polygon with a variable number of sides, ann−gon.
This notation can be used when referring to a polygon that does not have a special name in common use, like a
19 −gon. It can also be used when the number of sides of the polygon is unknown.

Key Exercise:

1. What is the measure of each interior angle of a regularn−gon if the sum of the interior angles is 1080 degrees?

Answer: 135 degrees

First the number of sides needs to be found:

1080 = 180 (n− 2 )

n= 8

Now the total of 1080 degrees needs to be divided into 8 congruent angles.

1080 ÷ 8 = 135

Sketchpad Alternatives –Many students become particularly engaged in a topic when they are able to investigate
it while playing around with the computer. Here are a couple of ways to use Geometers’ Sketchpad in the classroom
as an alternative or supplement to direct instruction.

Angle Sum Conjecture – Have student draw different convex polygons and measure the sum of their interior angles.

a. The students should observe that for each type of polygon, no matter how many were drawn, they all have the

same interior angle sum.

b. The students should drag a vertex of each polygon toward the center to create a concave polygon, and notice

if the sum stays the same. (It won’t.)

c. Put the sums in order on the board: 180, 360 , 540 ,...Ask the students to find the pattern in this sequence of

numbers. Lead them to discovering the Angle Sum formula from the pattern.

Exterior Angles

Clockwise or Counterclockwise But Not Both –At this point in the class, student are usually good at recognizing
vertical angles. They will understand that the exterior angles made by extending the sides of the polygon in a clock-
wise rotation are congruent, at each vertex, to the exterior angle formed by extending the sides counterclockwise.

Chapter 2. Geometry TE - Common Errors