2.4 - The Ins and Outs of Polygons

Objective:

The main focus of this problem is for you to be able to describe the difference between interior and exterior angles in a polygon, label polygons as being either "concave" or "convex" and to describe and use the relationship between interior and exterior angles.

Part 1: Launch

1.  Look at the two polygons pictured below and answer the following questions in your group:

• How are these two polygons different from the ones in the Shape Set?
• Look-up the definition of "convex" and "concave" polygons.  Which term describes the polygons below?  How do you know?
• In your square book, draw and label an example of a "convex polygon" and an example of a "concave polygon".

2.  Watch the video below and answer the following questions in your square book:

• How many sides does the track have?
• What is the sum of the "interior angles" of the track.  Clearly show your method.
• What is the relationship between the "interior angle" and the "exterior angle" for any one turn?
• What is the special name given to this special relationship?

Part 2: Explore

1. Work through Task A with your group.  Be sure to record your work on the handout provided in class: Labsheet 2.4 A.  Glue this page in your book.

2.  As a group, think about the following questions:

• What was the sum of the "exterior angles" for each polygon?
• Why do you think this is the case?  HINT - Think about which direction each cyclist is facing at the beginning of the race and at the end of the race.
• Work through Task C.  Be sure to show your thinking in your squarebook.

Part 3: Putting It All Together

1. Get a copy of Labsheet 2.4 D, glue it in your book, and answer the questions.  For each questions be sure to include the following:

• Write an equation to show the relationship between the sum of the three angles.
• Solve your equation using inverse operations and the property of equality.
• Use your solution to find the measure of each angle, be sure to show your work.
• Add the interior angles together to show that you have done your work correctly...be sure to think about what the sum of those angles should be.
• Use the "interior angles" to find the "exterior angles".  Add the "exterior angles" together to check your work...what should they add up to?

Part 4: Designing Stuff

1. Download and install a copy of TurtleArt found here.
2. Here are some basic tips on using TurtleArt.
3. Here are some advanced tips on using TurtleArt.
4. Try drawing the following polygons as an intro to TurtleArt
1. Square
2. Rectangle
3. Equilateral Triangle
4. Regular Hexagon

By the end of this problem, you should be able to do the following:

• Identify the difference between "concave" and "convex" polygons.
• Identify the difference between "interior" and "exterior" angles.
• Describe and show how to find the sum of the "interior angles" for any convex polygon.
• Know the sum of the "exterior angles" for any convex polygon.

HOMEWORK:

• 2.4 ACE (14, 15) (21) (25)
• Download and Install TurtleArt (the link is posted above)
• Quiz on Investigations 1 and 2 next class (that is everything in this unit so far)