Parallel Lines and Planes

Jason Wofsey, Oct 26, 2016

Table of Contents

  1. Paralle Lines
    1. Parallel Line Construction
    2. Skew Lines
    3. Parallel Plane Cut by Third Plane
    4. Lines Cut by Transversal
    5. Transversal Intersects Parallel Lines
    6. Exploring Corresponding Angles (V2)
    7. Alternate Interior Angles Theorem (V1)
    8. Same Side Interior Angles Theorem
    9. Alternate Exterior Angles Theorem (V1)
    10. Exploring Same Side Exterior Angles
    11. Animation 16
    12. Animation 39
    13. Animation 60
    14. Animation 29
    15. Animation 73
    16. Distance Between Parallel Lines
    17. Transversal Through 3 Parallel Lines
    18. Slope-Intercept Equation of Line
    19. Lines Perpendicular to Same Line but not Parallel
  2. Polygon Angles
    1. Polygons: Exterior Angles
    2. Convex vs. Concave
    3. Regular Polygon Action!
    4. Triangle Angle Theorems
  3. Slope
    1. Slope Triangle Rotation (VA)
    2. Point-Slope form of a Line
    3. Graphing point-slope form
    4. Graphing Line from Point-Slope Equation
    5. Point-Slope Practice

1.

Paralle Lines

  • 1. Parallel Line Construction
  • 2. Skew Lines
  • 3. Parallel Plane Cut by Third Plane
  • 4. Lines Cut by Transversal
  • 5. Transversal Intersects Parallel Lines
  • 6. Exploring Corresponding Angles (V2)
  • 7. Alternate Interior Angles Theorem (V1)
  • 8. Same Side Interior Angles Theorem
  • 9. Alternate Exterior Angles Theorem (V1)
  • 10. Exploring Same Side Exterior Angles
  • 11. Animation 16
  • 12. Animation 39
  • 13. Animation 60
  • 14. Animation 29
  • 15. Animation 73
  • 16. Distance Between Parallel Lines
  • 17. Transversal Through 3 Parallel Lines
  • 18. Slope-Intercept Equation of Line
  • 19. Lines Perpendicular to Same Line but not Parallel

1.1.

Parallel Line Construction

Construct a line parallel to the given line through point C.
– Jason Wofsey

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1.11.

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1.15.

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1.16.

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1.18.

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1.19.

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2.

Polygon Angles

  • 1. Polygons: Exterior Angles
  • 2. Convex vs. Concave
  • 3. Regular Polygon Action!
  • 4. Triangle Angle Theorems

2.1.

Polygons: Exterior Angles

The exterior angles of a triangle, quadrilateral, and pentagon are shown, respectively, in the applets below. [br][br]You can control the size of a colored exterior angle by using the slider with matching color. [br]Feel free to move the vertices of these polygons anywhere you'd like. [br][br][b]Note:[/b] [br]For the [b]quadrilateral[/b] & [b]pentagon[/b], the last two applets work best if these polygons are kept [b]convex.[/b][br]If you don't remember what this term means, [url=https://www.geogebra.org/m/knnPDMR3]click here for a refresher[/url].
Exterior Angles of a Triangle
Exterior Angles of a Quadrilateral
Exterior Angles of a Pentagon
What do you notice? What is common about the measures of the exterior angles of any one of these polygons?
Do you think what you've observed for the triangle, quadrilateral, and pentagon above will also hold true for a hexagon, heptagon, and octagon? [br][br]Create a new GeoGebra file and do some investigating to informally test your hypotheses!
– Tim Brzezinski

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3.

Slope

  • 1. Slope Triangle Rotation (VA)
  • 2. Point-Slope form of a Line
  • 3. Graphing point-slope form
  • 4. Graphing Line from Point-Slope Equation
  • 5. Point-Slope Practice

3.1.

Slope Triangle Rotation (VA)

[color=#000000]Interact with the applet below for a few minutes. [br]Then answer the questions that follow. [/color]
[color=#000000][i]Since [b][color=#38761D]a[/color][/b] and [b][color=#980000]b[/color][/b] represent lengths of segments, their values are non-negative! [br]Keep this in mind as you answer the questions below. [/i][br][br][/color]
1.
What is the slope of line j? Write this slope in terms of [b][color=#38761D]a[/color][/b] and [b][color=#980000]b[/color][/b].
2.
What is the measure of the [b][color=#666666]gray angle[/color][/b]? How do you know this?
3.
What is the sum of the measures of the [b][color=#1e84cc]blue acute angle[/color][/b] and [b][color=#ff00ff]pink acute angle[/color][/b]? Explain how you clearly know this to be true.
4.
What is the slope of line k in the applet above? Write this slope in terms of [b][color=#38761D]a[/color][/b] and [b][color=#980000]b[/color][/b].
5.
What can you conclude about 2 (non-horizontal & non-vertical) perpendicular lines drawn in the coordinate plane?
Quick (Silent) Demo
– Tim Brzezinski

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