Polygons & Angles

Tim Brzezinski, Dawn White, Nov 8, 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
    6. Heptagon Angle Theorems
    7. Octagon 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
    5. Exterior Angles of a Heptagon
    6. Exterior Angles of an Octagon
  4. Other & Older Versions of Applets in Chapter 1
    1. Triangle Angle Theorems (V3)
    2. Triangle Interior & Exterior Angle Sum Theorems (II)
    3. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
    4. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
    5. Pentagon Interior & Exterior Angle Sum Theorems
    6. Hexagon Interior & Exterior Angle Sum Theorems
    7. Heptagon Interior & Exterior Angle Sum Theorems
    8. Octagon Interior & Exterior Angle Sum Theorems
    9. Exterior Angles of Polygons--Proofs without Words
  5. 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
  • 6. Heptagon Angle Theorems
  • 7. Octagon 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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2.6.

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2.7.

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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
  • 5. Exterior Angles of a Heptagon
  • 6. Exterior Angles of an Octagon

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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3.5.

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3.6.

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4.

Other & Older Versions of Applets in Chapter 1

  • 1. Triangle Angle Theorems (V3)
  • 2. Triangle Interior & Exterior Angle Sum Theorems (II)
  • 3. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
  • 4. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
  • 5. Pentagon Interior & Exterior Angle Sum Theorems
  • 6. Hexagon Interior & Exterior Angle Sum Theorems
  • 7. Heptagon Interior & Exterior Angle Sum Theorems
  • 8. Octagon Interior & Exterior Angle Sum Theorems
  • 9. Exterior Angles of Polygons--Proofs without Words

4.1.

Triangle Angle Theorems (V3)

[b]Directions:[/b][br][br]Interact with the applet below for a few minutes.[br]Each time you move the slider, do so slowly. Pay careful attention to what you observe each time.[br][b][color=#1551b5]Be sure to move the [/color][color=#444]black vertices[/color] [color=#1551b5]of the triangle around each time after you reset the slider! [/color] [/b][br][br][i]Be sure to answer the questions that will appear in the applet. [/i]
– Tim Brzezinski

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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5.

Basic Illustrations

  • 1. Triangle Angle Sum Theorem

5.1.

Triangle Angle Sum Theorem

– Tim Brzezinski

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