Polygons & Angles
Contains interactive applets pertaining to interior and exterior angles of polygons. Book written largely by Tim Brzezinski, with edits by John Williams
Table of Contents
- Classifying Polygons
- Convex vs. Concave
- Polygon Interior & Exterior Angle Sum Theorems
- Triangle Angle Theorems
- Quadrilateral Angle Theorems
- Pentagon Angle Theorems
- Hexagon Angle Theorems
- Polygon Exterior Angle Sum Theorems (Easier to See)
- Exterior Angles of a Triangle
- Exterior Angles of a Quadrilateral
- Exterior Angles of a Pentagon
- Exterior Angles of a Hexagon
- Exterior Angles of a Heptagon
- Exterior Angles of an Octagon
Convex vs. Concave
In the applets below,[br][br]Any polygon that is [color=#ff7700][b]orange[/b][/color] is a [color=#ff7700][b]CONVEX POLYGON.[/b] [br][/color]Any polygon that is [color=#1e84cc][b]blue[/b][/color] is a [b][color=#1e84cc]CONCAVE POLYGON. [br][br][/color][/b]Interact with these applets for a few minutes. [br]As you do, be sure to move the polygon's BIG WHITE VERTICES AROUND! [br]Then, answer the questions that follow.
1.
2.
1.
According to the 2nd applet, 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]?
2
Take another look at the 1st applet. How could you define the terms [i][color=#ff7700][b]convex[/b][/color][/i] and [i][color=#1e84cc][b]concave[/b][/color][/i] with respect to the segment "inside" the polygon?
3.
Is it ever possible for a triangle to be [color=#1e84cc][b]concave[/b][/color]? Why or why not?
Triangle Angle Theorems
[color=#000000]Interact with the applet below for a few minutes. [br]Then, answer the questions that follow. [br][br][/color][i][color=#980000]Be sure to change the locations of the triangle's WHITE VERTICES each time before you drag the slider!!! [/color][/i]
1) What geometric transformations took place in the applet above?
[color=#000000]2) When working with the triangle's interior angles, did any of these transformations [br] change the measures of the [/color][color=#0000ff]blue[/color] [color=#000000]or[/color] [color=#6aa84f]green[/color] [color=#000000]angles?[/color]
3) From your observations, what is the sum of the measures of the interior angles of [i]any triangle? [/i]
[color=#000000]4) When working with the triangle's exterior angles, did any of these transformations change the measures of the [/color][color=#6aa84f]green[/color][color=#000000] or [/color][color=#999999]gray[/color][color=#000000] angles?[/color]