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

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- anonymous

@johnweldon1993 can u please help me !!!

- anonymous

@mathmate please please help me

- mathmate

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## More answers

- anonymous

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

- mathmate

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?

- anonymous

yes I am (:

- mathmate

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

- mathmate

* we need to prove that mAD = mBC

- mathmate

@Moo_Moo17
What do you think the approach would be?

- anonymous

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

- mathmate

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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

@mathmate im some what fimilar with the tools really sorry

- mathmate

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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

- anonymous

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

- mathmate

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

- anonymous

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

- mathmate

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].

- anonymous

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

- mathmate

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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

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

- anonymous

@mathmate

- mathmate

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.

- anonymous

I sorta have I wasn't very good at it

- mathmate

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

- mathmate

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

- anonymous

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

- mathmate

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Consider the above diagram.

- mathmate

@Moo_Moo17 you there?

- anonymous

yea i am sorry

- mathmate

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

- mathmate

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

- mathmate

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

- jim_thompson5910

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.

##### 1 Attachment

- anonymous

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

- mathmate

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

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