Polyon Interior Angles: Investigations
Polygon Interior Angles: Discovery Learning Explorations for GeoGebra Classroom
Table of Contents
- Triangle
- Triangle: Interior Angles (Revamped)
- Quadrilateral
- Quadrilateral Interior Angles (Revamped)
- Pentagon
- Pentagon: Interior Angles
- Building Further
- Polygon Interior Angles: Continued...
Triangle: Interior Angles (Revamped)
Interact with this app for a few minutes. Then answer the questions that follow. [br]Note: [b]LARGE POINTS[/b] are moveable.
What do you notice here? What do you wonder?
Try to get the vertices of the triangle's 3 angles to coincide (lie on top of each other). Move these sectors (circle pieces) around so they don't overlap. Notice anything interesting? If so, describe.
Quadrilateral Interior Angles (Revamped)
Interact with this app for a few minutes. Then answer the questions that follow. [br]Note: [b]ALL [/b][b]LARGE POINTS[/b] are moveable.
What do you notice here? What do you wonder?
Try to get the vertices of the 4 angles to coincide (lie on top of each other). Move these sectors (circle pieces) around so they don't overlap. Notice anything interesting? If so, describe.
Pentagon: Interior Angles
[color=#000000]Interact with the app below for a few minutes. Then answer the questions that follow. [br][br]Be sure to change the locations of the pentagon's [b]VERTICES[/b] each time [i]before[/i] you drag the slider. [br][br]Note: The points on the pentagon's sides are [i]midpoints. [/i][/color]
What geometric transformations took place in the app above?
[color=#000000]Did any of these transformations change the measures of these interior [/color][color=#000000]angles? If so, explain how. If not, explain why not. [/color]
From your observations, what is the sum of the measures of the interior angles of [i]any pentagon? [/i]
Polygon Interior Angles: Continued...
So far, you've explored the sum of the interior angles of a triangle, quadrilateral, and pentagon. Fill in the 2nd column below for these 3 polygons.
What do you think the sum of the measures of the interior angles of a hexagon will be? Why do you think this is true?
Construct a hexagon in this app below and find and display the sum of the measures of its interior angles. Do your results confirm what you predicted above?
What do you think the sum of the measures of the interior angles of a heptagon will be? What about an octagon? Why do you claim this?
Test your hypothesis for the heptagon below. Do your results confirm what you predicted above?
Test your hypothesis for the octagon below. Do your results confirm what you predicted above?
Suppose a polygon has 85 sides. What would the sum of its interior angle measures be? Explain your reasoning. Be sure to include this value in the table above.
Suppose a polygon has [i]N[/i] sides. What would the sum of its interior angle measures be (in terms of [i]N[/i])? Explain your reasoning. Be sure to include this expression in the table above.