Polygon Angles Exploration!
Polygon Angles Exploration!
Table of Contents
- Triangle
- Triangle Interior and Exterior Angles: Quick Exploration
- Triangle
- Quadrilateral
- Quadrilateral Interior and Exterior Angles: Quick Exploration
- Quadrilateral
- Pentagon
- Pentagon Interior and Exterior Angles: Quick Exploration
- Pentagon
- Hexagon
- Hexagon Interior and Exterior Angles: Quick Exploration
- Hexagon
- Heptagon
- Heptagon
- Octagon
- Octagon
- Data Gathering
- Let's Gather Your Data Now
Triangle Interior and Exterior Angles: Quick Exploration
In the Geometry app below,
[size=150]1) Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct triangle [i]ABC[/i]. [br]2) Select the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool. Then click anywhere inside the polygon. [br]3) Go to the Algebra view (click calculator icon upper left). [br][br]4) Calculate the sum of the measures of the interior angles of this triangle. [i]Be sure to add the [br] Greek letters when doing so! [/i](See the video right below this app to see how to quickly do [br] this in GeoGebra). [br][/size]
Quick (Silent) Demo
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool in the app above. Move any one (or more) of the triangle's vertices around. What can we conclude about the [b]sum of the measures of the interior angles[/b] of any triangle? [/size]
Here, in this app, we have a triangle with its EXTERIOR ANGLES shown. Calculate the SUM of the measures of these exterior angles here in this app.
Question 2
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the triangle's vertices around. [br]What can we conclude about the [b]exterior angles[/b] of this triangle? [i]Be specific in your response. [/i][/size]
Quadrilateral Interior and Exterior Angles: Quick Exploration
In the Geometry app below,
[size=150]1) Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct quadrilateral [i]ABCD[/i]. [br]2) Select the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool. Then click anywhere inside the polygon. [br]3) Go to the Algebra view (click calculator icon upper left). [br][br]4) Calculate the[b] sum of the measures of the interior angles of this quadrilateral[/b], making [br] sure to add the Greek letters (and not single numerical values)! If you forget how to do this, [br] [url=https://youtu.be/v2tYFqcShSg]click here to see it again the context of a triangle[/url]. [/size]
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool in the app above. Move any one (or more) of the triangle's vertices around. What can we conclude about the [b]sum of the measures of the interior angles[/b] of any quadrilateral? [/size]
Here, in this app, we have a quadrilateral with its EXTERIOR ANGLES shown. Calculate the SUM of the measures of these exterior angles here in this app.
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the triangle's vertices around. [br]What can we conclude about the [b]exterior angles[/b] of this quadrilateral? [i]Be specific in your response. [/i][/size]
Pentagon Interior and Exterior Angles: Quick Exploration
In the Geometry app below,
[size=150]1) Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct pentagon [i]ABCDE[/i]. [br]2) Select the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool. Then click anywhere inside the polygon. [br]3) Go to the Algebra view (click calculator icon upper left). [br][br]4) Calculate the[b] sum of the measures of the interior angles of this pentagon[/b], making [br] sure to add the Greek letters (and not single numerical values)! If you forget how to do this, [br] [url=https://youtu.be/v2tYFqcShSg]click here to see it again in the context of a triangle[/url]. [/size]
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool in the app above. Move any one (or more) of the triangle's vertices around. What can we conclude about the [b]sum of the measures of the interior angles[/b] of any pentagon? [/size]
Here, in this app, we have a pentagon with its EXTERIOR ANGLES shown. Calculate the SUM of the measures of these exterior angles here in this app.
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the triangle's vertices around. [br]What can we conclude about the [b]exterior angles[/b] of this pentagon? [i]Be specific in your response. [/i][/size]
Hexagon Interior and Exterior Angles: Quick Exploration
In the Geometry app below,
[size=150]1) Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct hexagon [i]ABCDEF[/i]. [br]2) Select the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool. Then click anywhere inside the polygon. [br]3) Go to the Algebra view (click calculator icon upper left). [br][br]4) Calculate the[b] sum of the measures of the interior angles of this hexagon[/b], making [br] sure to add the Greek letters (and not single numerical values)! If you forget how to do this, [br] [url=https://youtu.be/v2tYFqcShSg]click here to see it again in the context of a triangle[/url]. [/size]
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool in the app above. Move any one (or more) of the triangle's vertices around. What can we conclude about the [b]sum of the measures of the interior angles[/b] of any hexagon? [/size]
Here, in this app, we have a hexagon with its EXTERIOR ANGLES shown. Calculate the SUM of the measures of these exterior angles here in this app.
[size=150]Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the triangle's vertices around. [br]What can we conclude about the [b]exterior angles[/b] of this hexagon? [i]Be specific in your response. [/i][/size]
Heptagon
Interact with this app for a few minutes. Be sure to move the heptagon's vertices around each time you decide to re-slide the slider!
What would the sum of the measures of the interior angles of a heptagon be? [br]How about the sum of its exterior angles? [br][br]Explain your logic...
Octagon
Interact with this app for a few minutes. Be sure to move the octagon's vertices around each time you decide to re-slide the slider!
Write 2 similar conclusions here that are similar to the conclusions you've made about the past few polygons you've studied? [br][i][br]What two facts can we intuitively conclude about an octagon here? [/i]
Let's Gather Your Data Now
[size=200][url=https://docs.google.com/document/d/1S_w2xBTMEzhWjef_IepIj1BpTXf_jQ_qqDIX-f0VMZM/copy]Use your results from this investigation to complete this activity now[/url]. [/size]