Geometry: Parallel Lines & Related Angles

Tim Brzezinski, Katie Fay, Ramona Teodorescu, Oct 14, 2016

Table of Contents

  1. Transversal Intersects Parallel Lines: Scenarios
    1. Transversal Intersects Parallel Lines
    2. Exploring Corresponding Angles (V2)
    3. Alternate Interior Angles Theorem (V1)
    4. Alternate Exterior Angles Theorem (V1)
    5. Same Side Interior Angles Theorem
    6. Exploring Same Side Exterior Angles
    7. Exploring Alternate Interior Angles (V2)
    8. Alternate Interior Angles Theorem (V3)
    9. Exploring Alternate Exterior Angles (V2)
    10. Alternate Exterior Angles Theorem (V3)
    11. Solution to Parallel Lines & Angles Problem
  2. Angle Position Names When Transversal Intersects Lines
    1. Naming Angle Positions
    2. Parallel Lines & Related Angles

1.

Transversal Intersects Parallel Lines: Scenarios

  • 1. Transversal Intersects Parallel Lines
  • 2. Exploring Corresponding Angles (V2)
  • 3. Alternate Interior Angles Theorem (V1)
  • 4. Alternate Exterior Angles Theorem (V1)
  • 5. Same Side Interior Angles Theorem
  • 6. Exploring Same Side Exterior Angles
  • 7. Exploring Alternate Interior Angles (V2)
  • 8. Alternate Interior Angles Theorem (V3)
  • 9. Exploring Alternate Exterior Angles (V2)
  • 10. Alternate Exterior Angles Theorem (V3)
  • 11. Solution to Parallel Lines & Angles Problem

1.1.

Transversal Intersects Parallel Lines

[b][color=#980000]Students:[/color][/b][br][br]Use the GeoGebra applet above to help you complete the [b][color=#1e84cc]Transversals, Lines, & Related Angles[/color][/b] investigation given to you at the beginning of class.
– Tim Brzezinski

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1.9.

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1.11.

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2.

Angle Position Names When Transversal Intersects Lines

  • 1. Naming Angle Positions
  • 2. Parallel Lines & Related Angles

2.1.

Naming Angle Positions

Definition: A transversal is a line that intersects 2 other lines at 2 distinct points. [br][br]In the applet, the dashed line below is a transversal. (Actually, each of the three lines displayed below is a transversal.)[br][br]When a transversal intersects 2 other lines, special names are given to certain pairs of angles. [br]These angle pairs are called [b]corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles, and same-side exterior angles[/b]. [br][br]Explore these angle pairs within the applet below. Then, answer the questions that follow.
Questions:[br][br]1) What does the term "same-side" mean in the phrases "same-side interior angles" and "same-side exterior angles"? [br]2) What does the term "alternate" mean in the phrases "alternate interior angles" and "alternate exterior angles"? [br]3) Which of the four displayed angles would be considered "interior" angles? Why is this?[br]4) Which of the four displayed angles would be considered "exterior" angles? Why is this?[br]5) How would you describe, in your own words, what it means for a pair of angles to be described as "corresponding angles"?
– Tim Brzezinski

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