Geometry
Name: ________________________________________
Ch. 8: Quadrilaterals
Investigate: Interior Angle Sum Theorem
Date: _________________________________________
Essential Question: What is the sum of the measures of the interior angles of a convex n-gon?
Step 1: Convex polygons with 3-8 sides have been drawn for you in the chart below.
Step 2: You can use triangles and the Triangle Angle-Sum Theorem to find the sum of the measures of the angles of a polygon.
In each polygon, draw all diagonals from one vertex. A diagonal is a segment that joins two non-adjacent vertices. Notice the
diagonal divides the polygon into triangles.
Step 3: By the Triangle Angle Sum Theorem, the sum of the angles of a triangle is 180º. Use this theorem to complete the chart
below.
Polygon
# of Sides
# of Triangles Formed
Step 4: Draw conclusions.
a.) Look for patterns in the table. Describe any that you find.
Sum of Interior Angle
Measures
b.) Using the patterns you found, what is the sum of the interior angles of a convex decagon?
c.) Inductive Reasoning- Write a rule for the sum of the measures of the angles of an n-gon.
d.) Extension- Do you think the side lengths of the polygon affect the sum of the interior angles? Why or why not?