A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Write an indirect proof to show that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @johnweldon1993 can u please help me !!!

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathmate please please help me

  3. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you have the original question?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no all it telling is to Write an indirect proof to show that opposite sides of a parallelogram are congruent

  5. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok. To start, congruent opposite sides of a parallelogram is one of the properties of a parallelogram. Since we need to prove it, we have to start with the definition of a parallelogram to know what we already know. According to Wiki: "In Euclidean geometry, a parallelogram is a (non self-intersecting) quadrilateral with two pairs of parallel sides. " Are you familiar with congruent triangles, and transversals of parallel lines?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes I am (:

  7. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Good, so this is what we're given with. |dw:1433891186196:dw| We need to prove that AD // BC

  8. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    * we need to prove that mAD = mBC

  9. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Moo_Moo17 What do you think the approach would be?

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im not sure I feel like I know it but I cant remember sorry im trying

  11. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433891607737:dw| The trick is to draw the diagonal BD, then you could prove that triangles ABD and CDB are congruent. Since AD and BC are corresponding sides, they would be congruent. I'll let you attempt that, since you are familiar with the tools needed (parallel lines, transversals, congruent triangles).

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathmate im some what fimilar with the tools really sorry

  13. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433892491187:dw| You would prove congruence by ASA. Look up your notes to find the justifications for angle ABC = angle CDB ....[justification] BD=BD ....[justification] angle BDA = angle DBC ....[justification] Therefore triangles ABD and CDB are congruent [ASA, or angle-side-angle] and mAB=mCD [corresponding sides of congruent triangles]. You can use the following link as a review. http://www.mathsisfun.com/geometry/triangles-congruent-finding.html

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok the answer would triangles ABD and CDB are congruent [ASA, or angle-side-angle] and mAB=mCD [corresponding sides of congruent triangles].

  15. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You still need 3 justifications that I left blank to complete the proof.

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok so so the 1 is ASA I think 2 m not to sure what it would be 3 SSS I think

  17. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You only have to fill in the red parts to complete the proof. The rest is already done for you. Use the link if necessary to find the justifications: http://www.mathsisfun.com/geometry/triangles-congruent-finding.html angle ABC = angle CDB ....[\(\color{red}{justification}\)] BD=BD ....[\(\color{red}{justification}\)] angle BDA = angle DBC ....[\(\color{red}{justification}\)] Therefore triangles ABD and CDB are congruent [ASA, or angle-side-angle] and mAB=mCD [corresponding sides of congruent triangles].

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im trying to figure it out but im having trouble can u please help me I don't understand

  19. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433895706289:dw| When a transversal cuts two parallel lines, it makes many congruent angles, out of which: Vertically opposite angles are: a=d, b=c, f=g, e=h corresponding angles a=e, c=g b=f, d=h alternate interior angles c=f, d=e Alternate exterior angles a=h, b=g It seems a lot, but if you study it, they are all logical groups. If you work with those, you will find the justifications not too hard to find.

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so ABC = CDB are Vertically opposite angles angle BDA = DBC is Corresponding angles Angle BD= BD is think alternate interior angles

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathmate

  22. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry, not quite. You need to see how the groups work. BD is not even an angle. BTW, have you done geometric proofs before? It seems that you're quite rusty about it.

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I sorta have I wasn't very good at it

  24. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It would be a good idea to study and understand the link I gave you, and then you'll be better at it. No efforts, no results. http://www.mathsisfun.com/geometry/triangles-congruent-finding.html

  25. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and this one for congruent angles: https://www.mathsisfun.com/geometry/parallel-lines.html

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idk i just idk im sorry im so confused im very good geometry iv studied and studied but im not good at anything

  27. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1433900762255:dw| Consider the above diagram.

  28. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Moo_Moo17 you there?

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea i am sorry

  30. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No sorry, it took me a while to come back, sorry about that.

  31. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Seeing that BC is parallel to AD, what can you say about angles ADB and DBC?

  32. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    They are equal, because they are alternate interior angles. (read the second link)

  33. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Here is a guide to show you that one pair of sides are congruent. I leave the rest of the proof for you to do on your own. You'll have similar steps to mine that I show in the attached pdf.

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    BC is congruent to AD but also i think they are corresponding angles or transversal

  35. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    AD is equal to AD with the justification "common", because it's the same length.

  36. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.