Polygons & Angles

Tim Brzezinski, Aaron Dankman, Nov 10, 2016

Contains interactive applets pertaining to interior and exterior angles of polygons.

Table of Contents

  1. Classifying Polygons
    1. Convex vs. Concave
  2. Polygon Interior & Exterior Angle Sum Theorems
    1. Triangle Angle Theorems
    2. Triangle Angle Theorems (V2)
    3. Quadrilateral Angle Theorems
    4. Pentagon Angle Theorems
    5. Hexagon Angle Theorems
  3. Polygon Exterior Angle Sum Theorems (Easier to See)
    1. Exterior Angles of a Triangle
    2. Exterior Angles of a Quadrilateral
    3. Exterior Angles of a Pentagon
    4. Exterior Angles of a Hexagon
  4. Basic Illustrations
    1. Triangle Angle Sum Theorem

1.

Classifying Polygons

  • 1. Convex vs. Concave

1.1.

Convex vs. Concave

In the app below, move the vertices of the shown polygon around. Be sure to explore the triangle, quadrilateral, and pentagon. Then, answer the questions that follow.
According to the app, how would you describe what it means for a polygon to be [color=#ff7700][b]convex[/b][/color]? How would you describe what it means for a polygon to be [color=#1e84cc][b]concave[/b][/color]?
Is it ever possible for a triangle to be [color=#1e84cc][b]concave[/b][/color]? Why or why not?
– Tim Brzezinski

2.

Polygon Interior & Exterior Angle Sum Theorems

  • 1. Triangle Angle Theorems
  • 2. Triangle Angle Theorems (V2)
  • 3. Quadrilateral Angle Theorems
  • 4. Pentagon Angle Theorems
  • 5. Hexagon Angle Theorems

2.1.

Triangle Angle Theorems

Interact with the app below for a few minutes.  [br]Then, answer the questions that follow.  [br][br]Be sure to change the locations of this triangle's vertices each time [i]before[/i] you drag the slider!
What is the [b]sum of the measures of the interior angles of this triangle? [/b]
What is the [b]sum of the measures of the exterior angles [/b]of this triangle?
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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2.5.

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3.

Polygon Exterior Angle Sum Theorems (Easier to See)

  • 1. Exterior Angles of a Triangle
  • 2. Exterior Angles of a Quadrilateral
  • 3. Exterior Angles of a Pentagon
  • 4. Exterior Angles of a Hexagon

3.1.

Exterior Angles of a Triangle

– Tim Brzezinski

3.2.

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3.3.

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3.4.

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4.

Basic Illustrations

  • 1. Triangle Angle Sum Theorem

4.1.

Triangle Angle Sum Theorem

– Tim Brzezinski

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