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Roosevelt Middle School

  1. I can prove two lines are parallel given they are both parallel to a same 3rd line.
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    • Pause the video and take a moment to think through how you would prove this.
      1. Plan for proof: Use angle pair relationship to show 1 and 2 are congruent; use angle pair to show 3 and 4 are congruent. Then make a connection using vertical angles 2 and 4 with the transitive property to show 1 and 3 are congruent. A converse the
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    • From this point on, you can call this idea we are proving the "3rd parallel theorem" in a proof.
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    • What if I had done angles 1 and 4 in my proof? Would that have made this proof shorter?
      1. Yes, we could have totally skipped the vertical angles and just done the transitive property once.
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    • My proof could have been two steps shorter if...
      1. I used either corresponding angles theorem with 1 and 4 or alternate exterior angles theorem on angles 2 and 3.
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