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hhopke

  • one year ago

Prove that QR || US

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  1. hhopke
    • one year ago
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  2. mathstudent55
    • one year ago
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    What do you need to show to prove lines are parallel?

  3. hhopke
    • one year ago
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    ?

  4. hhopke
    • one year ago
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    That's what I have so far

  5. mathstudent55
    • one year ago
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    This is what I mean by the question above. Here are lines m and n, and transversal t. |dw:1434568617945:dw|

  6. hhopke
    • one year ago
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    But the picture doesn't look like that.

  7. mathstudent55
    • one year ago
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    Can you name a pair of angles in the figure below, that if you know they are congruent, then the lines m and n must be parallel? |dw:1434568719599:dw|

  8. hhopke
    • one year ago
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    There are a bunch (alt. ext, alt. int, corresponding, etc.) but I need to prove it with the given picture.|dw:1434568849868:dw|

  9. mathstudent55
    • one year ago
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    Ok. Great answer. I realize you are answering a different question with a different figure, but I needed to see if you knew how to prove lines parallel. Now I see that you do know.

  10. mathstudent55
    • one year ago
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    Let's look at your figure, and reason out the steps in this proof.

  11. mathstudent55
    • one year ago
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    |dw:1434569034493:dw|

  12. mathstudent55
    • one year ago
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    You need to prove lines QR and US parallel. If you could show that angles 2 and 6 are congruent, would that help?

  13. hhopke
    • one year ago
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    Yes.

  14. mathstudent55
    • one year ago
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    Correct bec angles 2 and 6 are corresponding angles, and if they are congruent, the lines are parallel.

  15. hhopke
    • one year ago
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    1 and 2 are alternate interior angles, so they are congruent (the lines are parallel) and 1 and 6 are congruent (given) so by transitive property 2 is congruent to 6 (that's how I did it)

  16. mathstudent55
    • one year ago
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    I marked the parallel lines and the given congruent angles. |dw:1434569202980:dw|

  17. mathstudent55
    • one year ago
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    We know angles 1 and 6 are congruent. We need to show that angles 2 and 6 are congruent.

  18. hhopke
    • one year ago
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    1 and 2 are alternate interior angles, so they are congruent (the lines are parallel) and 1 and 6 are congruent (given) so by transitive property 2 is congruent to 6

  19. mathstudent55
    • one year ago
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    Exactly. That is it.

  20. hhopke
    • one year ago
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    then 6 and 4 are congruent (vertical angles), so 4 is congruent to 1 and 2 (transitive property)

  21. hhopke
    • one year ago
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    is that useful?

  22. mathstudent55
    • one year ago
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    No. There is no need for 6 and 4

  23. hhopke
    • one year ago
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    okay.

  24. hhopke
    • one year ago
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    Now what?

  25. mathstudent55
    • one year ago
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    Since you can prove the lines parallel with corresponding congruent angles 2 and 6, there is no need to take the extra steps of showing that angles 4 and 6 are congruent by vertical angles and then the lines are parallel by angles 2 and 4 being congruen alt int angles.

  26. mathstudent55
    • one year ago
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    This is simpler proof than you originally thought.

  27. hhopke
    • one year ago
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    we can prove that they're parallel with 2 and 6?

  28. mathstudent55
    • one year ago
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    I'll go through your steps and we'll see what needs to be there.

  29. hhopke
    • one year ago
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    Okay.

  30. mathstudent55
    • one year ago
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    yes. 2 and 6 are corresponding angles. if you show that when two lines are cut by a transversal, corresp angles are congruent, then the lines are parallel.

  31. mathstudent55
    • one year ago
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    I'd keep statement 1, drop statements 2, 3. Keep statement 4.

  32. mathstudent55
    • one year ago
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    Drop statement 5.

  33. mathstudent55
    • one year ago
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    keep statement 6 and 7

  34. hhopke
    • one year ago
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    then drop 8 and add in the part about corresponding angles?

  35. mathstudent55
    • one year ago
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    drop 8 and 9. where 8 was, state that the lines are parallel bec of what I wrote above with corresp angles.

  36. hhopke
    • one year ago
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    Okay. Thank you so much!

  37. mathstudent55
    • one year ago
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    You're welcome.

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