Parallel Lines & Related Angles

Tim Brzezinski, Courtney O'Berry, Nov 15, 2016

Contains interactive applets involving transversal, lines, (parallel lines), and angles.

Table of Contents

  1. Transversal Intersects Parallel Lines: Scenarios
    1. Transversal Intersects Parallel Lines
    2. Corresponding Angles: Quick Investigation
    3. Congruent Corresponding Angles to Start? (Quick Investigation)
    4. Exploring Corresponding Angles (V2)
    5. Alternate Interior Angles: Quick Investigation
    6. Alternate Interior Angles Theorem (V1)
    7. Exploring Alternate Interior Angles (V2)
    8. Alternate Interior Angles Theorem (V3)
    9. Alternate Exterior Angles: Quick Investigation
    10. Alternate Exterior Angles Theorem (V1)
    11. Exploring Alternate Exterior Angles (V2)
    12. Alternate Exterior Angles Theorem (V3)
    13. Same-Side-Interior Angles: Quick Investigation
    14. Same Side Interior Angles Theorem
    15. Same-Side-Exterior Angles: Quick Investigation
    16. Exploring Same Side Exterior Angles
    17. Solution to Parallel Lines & Angles Problem
  2. Angle Position Names When Transversal Intersects Lines
    1. Naming Angle Positions
    2. Parallel Lines & Related Angles
  3. Parallel Lines & Similarity
    1. Effortless Trisections
    2. Parallel Lines Congruent Segments Theorem
    3. Parallel Lines Proportionality Theorem

1.

Transversal Intersects Parallel Lines: Scenarios

  • 1. Transversal Intersects Parallel Lines
  • 2. Corresponding Angles: Quick Investigation
  • 3. Congruent Corresponding Angles to Start? (Quick Investigation)
  • 4. Exploring Corresponding Angles (V2)
  • 5. Alternate Interior Angles: Quick Investigation
  • 6. Alternate Interior Angles Theorem (V1)
  • 7. Exploring Alternate Interior Angles (V2)
  • 8. Alternate Interior Angles Theorem (V3)
  • 9. Alternate Exterior Angles: Quick Investigation
  • 10. Alternate Exterior Angles Theorem (V1)
  • 11. Exploring Alternate Exterior Angles (V2)
  • 12. Alternate Exterior Angles Theorem (V3)
  • 13. Same-Side-Interior Angles: Quick Investigation
  • 14. Same Side Interior Angles Theorem
  • 15. Same-Side-Exterior Angles: Quick Investigation
  • 16. Exploring Same Side Exterior Angles
  • 17. 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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1.17.

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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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3.

Parallel Lines & Similarity

  • 1. Effortless Trisections
  • 2. Parallel Lines Congruent Segments Theorem
  • 3. Parallel Lines Proportionality Theorem

3.1.

Effortless Trisections

Interact with this app for a few minutes. Then, answer the questions that follow.
What can we conclude about the four lines shown? How do you know this to be true?
Explain the phenomenon you see here as best as you can in your own words.
You can use this space to help add to your explanation above.
– Tim Brzezinski

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Information