Geometry: Polygons & Angles

Tim Brzezinski, Brian Olmanson, Nov 30, 2015

Table of Contents

  1. Polygon Interior & Exterior Angle Sum Theorems
    1. Triangle Angle Theorems (V3)
    2. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
    3. Pentagon Interior & Exterior Angle Sum Theorems
    4. Hexagon Interior & Exterior Angle Sum Theorems
    5. Heptagon Interior & Exterior Angle Sum Theorems
    6. Octagon Interior & Exterior Angle Sum Theorems
  2. 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. Theorems: Proofs with Transformations
    1. Triangle Interior & Exterior Angle Sum Theorems (II)
  4. Basic Illustrations
    1. Triangle Angle Sum Theorem
  5. Others
    1. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
    2. Exterior Angles of Polygons--Proofs without Words

1.

Polygon Interior & Exterior Angle Sum Theorems

  • 1. Triangle Angle Theorems (V3)
  • 2. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
  • 3. Pentagon Interior & Exterior Angle Sum Theorems
  • 4. Hexagon Interior & Exterior Angle Sum Theorems
  • 5. Heptagon Interior & Exterior Angle Sum Theorems
  • 6. Octagon Interior & Exterior Angle Sum Theorems

1.1.

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

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

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

2.1.

Exterior Angles of a 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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3.

Theorems: Proofs with Transformations

  • 1. Triangle Interior & Exterior Angle Sum Theorems (II)

3.1.

Triangle Interior & Exterior Angle Sum Theorems (II)

[b][color=#c51414]Interact with the applet below for a few minutes.[br]Answer the questions that follow.[/color][br][/b]
[b][color=#c51414]Questions:[/color][/b][br][br]1) What can you conclude about a triangle's interior angle measures? [i]Be specific.[/i][br]2) What can you conclude about a triangle's exterior angle measures? [i]Be specific.[/i][br][br]3) [b]Use [/b][b][color=#c51414]transformational geometry[/color][/b] t[b]o prove your conclusions for both (1) and (2) are correct. [/b]
– Tim Brzezinski

4.

Basic Illustrations

  • 1. Triangle Angle Sum Theorem

4.1.

Triangle Angle Sum Theorem

– Tim Brzezinski

5.

Others

  • 1. Quadrilateral Interior & Exterior Angle Sum Theorems (V2)
  • 2. Exterior Angles of Polygons--Proofs without Words

5.1.

Quadrilateral Interior & Exterior Angle Sum Theorems (V2)

[b]Directions:[/b][br][br]Mess around with the applet below for a few minutes. [br]As you do, [b][color=#b20ea8]BE SURE TO DRAG THE PINK VERTICES around.[/color][/b] [br]As you move these [color=#b20ea8]pink vertices[/color] around, [b][i]be sure this quadrilateral stays CONVEX![/i][/b] [br][br][b]After interacting with this applet, please answer the questions that appear below it.[/b]
[b][color=#c51414]Questions:[/color][/b][br][br]1) What can you conclude about the [b]sum of the interior angle measures of a quadrilateral[/b]? Explain how you came to this conclusion. [br]2) What can you conclude about the [b]sum of the exterior angle measures of a quadrilateral[/b]? Explain how you came to this conclusion.
– Tim Brzezinski

5.2.

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