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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.
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.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@johnweldon1993 can u please help me !!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathmate please please help me

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Do you have the original question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no all it telling is to Write an indirect proof to show that opposite sides of a parallelogram are congruent

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Ok. 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 selfintersecting) quadrilateral with two pairs of parallel sides. " Are you familiar with congruent triangles, and transversals of parallel lines?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Good, so this is what we're given with. dw:1433891186196:dw We need to prove that AD // BC

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0* we need to prove that mAD = mBC

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@Moo_Moo17 What do you think the approach would be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not sure I feel like I know it but I cant remember sorry im trying

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0dw: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).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathmate im some what fimilar with the tools really sorry

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0dw: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 anglesideangle] and mAB=mCD [corresponding sides of congruent triangles]. You can use the following link as a review. http://www.mathsisfun.com/geometry/trianglescongruentfinding.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok the answer would triangles ABD and CDB are congruent [ASA, or anglesideangle] and mAB=mCD [corresponding sides of congruent triangles].

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0You still need 3 justifications that I left blank to complete the proof.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok so so the 1 is ASA I think 2 m not to sure what it would be 3 SSS I think

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0You 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/trianglescongruentfinding.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 anglesideangle] and mAB=mCD [corresponding sides of congruent triangles].

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im trying to figure it out but im having trouble can u please help me I don't understand

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0dw: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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so ABC = CDB are Vertically opposite angles angle BDA = DBC is Corresponding angles Angle BD= BD is think alternate interior angles

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I sorta have I wasn't very good at it

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0It 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/trianglescongruentfinding.html

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0and this one for congruent angles: https://www.mathsisfun.com/geometry/parallellines.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0idk i just idk im sorry im so confused im very good geometry iv studied and studied but im not good at anything

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433900762255:dw Consider the above diagram.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@Moo_Moo17 you there?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0No sorry, it took me a while to come back, sorry about that.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0Seeing that BC is parallel to AD, what can you say about angles ADB and DBC?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0They are equal, because they are alternate interior angles. (read the second link)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0Here 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0BC is congruent to AD but also i think they are corresponding angles or transversal

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0AD is equal to AD with the justification "common", because it's the same length.
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