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Week 13: Geometry - Polygons

Sum of Angles in a Polygon (Printable PDF)

What is the sum of the angles of a triangle? of a quadrilateral? of a pentagon? of a hexagon? What is the sum of the angles in convex polygons in terms of the number of sides? Move the mouse pointer over the picture for a hint.



Does the relationship for convex polygons also hold true for nonconvex polygons? Explain.



As seen in Problem Exploration

M6G1. Students will further develop their understanding of plane figures.

The definition of convex and nonconvex polygons will need to be understood.  Then various convex polygons will need to be constructed.

M6A2. Students will consider relationships between varying quantities.

a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.

The students can create tables with the columns: Polygon, # of Sides, # of Triangles, Sum of Degrees. The pattern can be generalized to (n-2) *180.

M7A3. Students will understand relationships between two variables.

a. Plot points on a coordinate plane.

b. Represent, describe and analyze relations from tables, graphs, and formulas.

The students can create a table with the number of sides of a polygon (x) in one column and the corresponding angle sum (y) in the other. Plot the points. The relationship is linear and is represented as y = 180x -360.

M8A4. Students will graph and analyze graphs of linear equations.
b. Determine the meaning of the slope and y-intercept in a given situation.
c. Graph equations of the form y = mx + b.
e. Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.


Extending from the above description, the students will need to determine that the relationship is linear, and determine the equation by finding the slope from 2 of the points, and then the y-intercept. The students will also need to discuss the domain of the problem and why the points on the line cannot be connected in a line (you cannot have 3.2 sides of a convex polygon – only whole numbers will work for this situation).