Investigation 2 Designing Polygons: The Angle Connection

Angle Sums of Regular Polygons Problem 2.1 Angle Sums of Regular Polygons Focus Question What is the size of each angle and the sum of all angles in a regular polygon with “n” sides? Memory Wall

Problem 2.1 Vocabulary Regular Polygon – a polygon in which all of the sides are the same length and all of the angles have the same measure. Irregular Polygon – not all of the sides are the same length or not all of the angles have the same measure

Can you pick all of the Regular Polygons out of the shape sets? Problem 2.1 Can you pick all of the Regular Polygons out of the shape sets? Which polygon has angles that appear to be the smallest? Which polygon has angles that appear to be the largest? Is there a relationship between the size of the angles and the number of sides for regular polygons? Video link

Problem 2.1A Use your angle ruler or protractor to measure the angles of the: 1)Equilateral Triangle 2)Square 3)Hexagon 4)Octagon Fill in your table, and calculate the angle sum.

Repeat your process for the Decagon Problem 2.1A What pattern do you see that might help you fill in the angle sum of the Pentagon? Test your hypothesis. (You may have to extend the lines of your pentagon to get an accurate angle measure) Repeat your process for the Decagon

Problem 2.1A Now try to use what you’ve learned to fill in the: a)Heptagon b)Nonagon 3)Describe a pattern relating angle sums to the number of sides in regular polygons

Problem 2.1A 4) Describe a pattern relating measures of individual angles and number of sides in regular polygons.

Problem 2.1B The diagram below shows two sets of regular polygons of different sizes. Does the pattern relating number of sides, measures of angles, and angle sums apply to all of these shapes? Explain your reasoning in your math notebook.

Problem 2.1C Explain how you could find the angle sum of a regular polygon with “n” sides. Write your conjecture as a formula S=___________ The right side of the equations should give an expression for calculating the sum from the value of “n”.

Problem 2.1D Explain how you could find the measure of each angle in a regular polygon with “n” sides. Write your conjecture as a formula A=________ The right side of the equation should give an expression for calculating the measure of each angle from the value of “n”.

Angle Sums of Regular Polygons Problem 2.1 Angle Sums of Regular Polygons Focus Question What is the size of each angle and the sum of all angles in a regular polygon with “n” sides? Memory Wall

(don’t forget to paste the worksheet for #2 into your Math Notebook) Problem 2.1 Home Assignment ACE Problems Pg 52 #1&2 (don’t forget to paste the worksheet for #2 into your Math Notebook)