Write an indirect proof to show that the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures.

- anonymous

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- anonymous

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- Compassionate

FLVS. 1.06?

- anonymous

*5.10

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- Compassionate

Mind sharing some notes ;D
Have you taken BiologY?

- anonymous

no i only do geometry work

- Compassionate

;-;
Sadface.
@hba might be able to help.

- anonymous

really ?

- anonymous

i was just talking to her today

- hba

@Compassionate
I was expecting something from you :/

- anonymous

does anyone know the answer?

- abb0t

4.20

- anonymous

@AravindG

- anonymous

@uri

- ganeshie8

its an indirect proof, so 3 steps :-
1) you start wid the opposite of wat u need to prove
2) arrive at a contradiction
3) conclude

- ganeshie8

since you wanto prove 'diagonals of a parallelogram bisect each other',
you start wid the opposite of above statement, like below :-
step1 :
Since we want to prove 'diagonals of a parallelogram bisect each other', lets start by assuming the opposite, that the diagonals of parallelogram dont bisect each other.

- ganeshie8

|dw:1378579736244:dw|

- ganeshie8

|dw:1378579847340:dw|

- anonymous

ok so now we got the figure

- ganeshie8

good :) Since, we assumed that the diagonals dont bisect each other,
\(OC \ne OA\)
\(OD \ne OB\)

- ganeshie8

Since, \(OC \ne OA\), \(\triangle OAD\) is not congruent to \(\triangle OCB\)

- ganeshie8

|dw:1378580084436:dw|

- anonymous

would this help me?https://www.google.com.qa/search?bav=on.2,or.r_qf.&bvm=bv.51773540,d.Yms,pv.xjs.s.en_US.jkEW54nYU50.O&biw=1600&bih=799&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=rHYrUrHaHsbQsgbbhYHYBg&q=an%20e%20qualaterla%20parallelo%20gram#hl=en&q=a+equilateral+parallelogram&spell=1&tbm=isch&um=1&facrc=_&imgdii=_&imgrc=mXpDHT_YPK_YEM%3A%3Bb4daeiFm_-fqfM%3Bhttp%253A%252F%252Fwww.gogeometry.com%252Fgeometry%252Fparallelogram_definition.gif%3Bhttp%253A%252F%252Fwww.gogeometry.com%252Fgeometry%252Fparallelogram_definition.htm%3B633%3B280

- ganeshie8

\(\angle AOD \cong \angle BOC\) as they are vertical angles,
\(\angle OAD \cong \angle OCB\) they are alternate interior angles
\(AD \cong BC\), by definition of parallelogram
so, by AAS, \(\triangle OAD\) is congruent to \(\triangle OCB\)

- anonymous

i think the one i should you is complicated rite

- ganeshie8

But, thats a contradiction as we have previously established that those triangles are congruent

- ganeshie8

step3 :-
since we arrived at a contradiction, our assumption is wrong. so, the opposite of our assumption must be correct. so diagonals of parallelogram bisect each other.

- ganeshie8

you want me go thru that link ?

- anonymous

yahh if you can

- ganeshie8

yeah wats wid that pic ? u wanto prove those theorems ?

- anonymous

should i write what you said in step 3?

- ganeshie8

yes any indirect proof must have all 3 steps

- anonymous

thelink is just a photo i thought was the same thing i was doing

- ganeshie8

assumption, contradiction, conclusion

- anonymous

##### 1 Attachment

- ganeshie8

hmm

- anonymous

step1 :
Since we want to prove 'diagonals of a parallelogram bisect each other', lets start by assuming the opposite, that the diagonals of parallelogram dont bisect each other.
step2: OC≠OA, △OAD is not congruent to △OCB
∠AOD≅∠BOC as they are vertical angles,
∠OAD≅∠OCB they are alternate interior angles
AD≅BC, by definition of parallelogram
step3 :-
since arrived at a contradiction, the assumption is wrong. so, the opposite of our assumption must be correct. so diagonals of parallelogram bisect each other.
so, by AAS, △OAD is congruent to △OCB

- anonymous

this is what i wrote/

- anonymous

but step 1 in my own words

- ganeshie8

wait a sec

- ganeshie8

u missed how u arrived at contradiction in step2

- anonymous

really ?
let me see

- anonymous

Since, we assumed that the diagonals dont bisect each other,
OC≠OA
OD≠OB

- anonymous

this is it rite?

- ganeshie8

step1 :
Since we want to prove 'diagonals of a parallelogram bisect each other', lets start by assuming the opposite, that the diagonals of parallelogram dont bisect each other.
step2:
Since, we assumed that the diagonals dont bisect each other,
OC≠OA
OD≠OB
Since, OC≠OA, △OAD is not congruent to △OCB
∠AOD≅∠BOC as they are vertical angles,
∠OAD≅∠OCB they are alternate interior angles
AD≅BC, by definition of parallelogram
so, by AAS, △OAD is congruent to △OCB
But, thats a contradiction as we have previously established that those triangles are NOT congruent
step3 :-
since arrived at a contradiction, the assumption is wrong. so, the opposite of our assumption must be correct. so diagonals of parallelogram bisect each other.

- anonymous

WOW! thank you ! in the photo i posted there was question 5 i think the answer is both lines intersect each other am i rite?

- ganeshie8

question 4 itself is asking u to prove diagonals bisect each other

- anonymous

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- anonymous

sorry i meant 5 xD

- anonymous

lol im so clumsy

- ganeshie8

u have geogebra ?

- anonymous

yes

- anonymous

but not rite now on my laptop

- ganeshie8

ohk

- anonymous

should i download it ?

- ganeshie8

##### 1 Attachment

- ganeshie8

pfa pic
there we have a small rectangle with y axis going thru its senter
and a dilated rectangle,

- anonymous

so those are the 2 figures

- ganeshie8

yes, observe that for the big rectangle also, the y axis is going thru center

- anonymous

so the new figure is overlapping ?

- ganeshie8

yes, but that doesnt matter, the thing to notice here is that, both figures have the same center

- ganeshie8

y-axis is going thru both the centers... so dilation didnt affect this center line EF

- ganeshie8

why ?

- anonymous

ow ok so overlapping is wrong

- ganeshie8

read the q once, the q is asking you about the center line.
the q is not about whether the figures overlapping or not

- anonymous

ok so both figures have the same center. y-axis is going thru both the centers so dilation didnt affect this center line EF

- ganeshie8

looks good :) and add some more reasoning if u can think a bit more...

- anonymous

ok :) thx Another question is about a figure that i should find out the error should i explain it or just show you

- anonymous

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