1.6 Quadrilaterals
Interior Angles
Pacing:This lesson should take one class period
Goal: Students will use the Triangle Sum Theorem to derive the Polygonal Sum Theorem by dividing a convex
polygon into triangles.
Inquiry Based Learning! Analyzing a pattern is another method to looking at the polygonal sum theorem. Begin
by setting up the below chart. Ask students to fill in the second column, asking if the number of side lengths can
form a polygon. Ask students to then complete the obvious interior angle sums such as triangle and quadrilateral.
Encourage students to see a pattern and create its function.Students should see that the “starting” sum is 180 and
each subsequent polygonal sum is180 degreesgreater.
Vocabulary!Reiterate to students that a diagonal is drawn from any vertex to a non-adjacent vertex.
Extension!Does this theorem work for non-convex polygons? Pose this question to students as you draw several
non-convex polygons on the board.Since the polygon is non-convex, the “indented” angle will always be obtuse,
showing this theorem will only work for convex polygons.
Additional Example:The sum of the interior angles of ann−gon is 3,960 degrees.What isn?n= 24
Exterior Angles
Pacing:This lesson should take one class period
Goal:This lesson introduces students to exterior angles of polygons. The Linear Pair Theorem is used to determine
the measures of exterior angles.
Stress to students that there are two possibilities for exterior angles and it will be extremely important to label the
angle correctly.
Additional Examples:Using what you have learned thus far, determine the measure of^6 F GH.Students will use the
Polygonal Sum Theorem to determine the sum of the interior angles in the heptagon is 900 ◦. Dividing by 7 , each
interior angle has a measure of 128. 57 ◦.^6 F GH forms a linear pair with^6 AGF and are supplementary. Therefore,
the measure of angle F GH= 51 .43 degrees.
Chapter 1. Geometry TE - Teaching Tips