anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
1 Attachment
Compassionate
  • Compassionate
FLVS. 1.06?
anonymous
  • anonymous
*5.10

Looking for something else?

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

More answers

Compassionate
  • Compassionate
Mind sharing some notes ;D Have you taken BiologY?
anonymous
  • anonymous
no i only do geometry work
Compassionate
  • Compassionate
;-; Sadface. @hba might be able to help.
anonymous
  • anonymous
really ?
anonymous
  • anonymous
i was just talking to her today
hba
  • hba
@Compassionate I was expecting something from you :/
anonymous
  • anonymous
does anyone know the answer?
abb0t
  • abb0t
4.20
anonymous
  • anonymous
@AravindG
anonymous
  • anonymous
@uri
ganeshie8
  • 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
  • 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
  • ganeshie8
|dw:1378579736244:dw|
ganeshie8
  • ganeshie8
|dw:1378579847340:dw|
anonymous
  • anonymous
ok so now we got the figure
ganeshie8
  • ganeshie8
good :) Since, we assumed that the diagonals dont bisect each other, \(OC \ne OA\) \(OD \ne OB\)
ganeshie8
  • ganeshie8
Since, \(OC \ne OA\), \(\triangle OAD\) is not congruent to \(\triangle OCB\)
ganeshie8
  • ganeshie8
|dw:1378580084436:dw|
anonymous
  • 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
  • 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
  • anonymous
i think the one i should you is complicated rite
ganeshie8
  • ganeshie8
But, thats a contradiction as we have previously established that those triangles are congruent
ganeshie8
  • 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
  • ganeshie8
you want me go thru that link ?
anonymous
  • anonymous
yahh if you can
ganeshie8
  • ganeshie8
yeah wats wid that pic ? u wanto prove those theorems ?
anonymous
  • anonymous
should i write what you said in step 3?
ganeshie8
  • ganeshie8
yes any indirect proof must have all 3 steps
anonymous
  • anonymous
thelink is just a photo i thought was the same thing i was doing
ganeshie8
  • ganeshie8
assumption, contradiction, conclusion
anonymous
  • anonymous
1 Attachment
ganeshie8
  • ganeshie8
hmm
anonymous
  • 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
  • anonymous
this is what i wrote/
anonymous
  • anonymous
but step 1 in my own words
ganeshie8
  • ganeshie8
wait a sec
ganeshie8
  • ganeshie8
u missed how u arrived at contradiction in step2
anonymous
  • anonymous
really ? let me see
anonymous
  • anonymous
Since, we assumed that the diagonals dont bisect each other, OC≠OA OD≠OB
anonymous
  • anonymous
this is it rite?
ganeshie8
  • 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
  • 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
  • ganeshie8
question 4 itself is asking u to prove diagonals bisect each other
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
sorry i meant 5 xD
anonymous
  • anonymous
lol im so clumsy
ganeshie8
  • ganeshie8
u have geogebra ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
but not rite now on my laptop
ganeshie8
  • ganeshie8
ohk
anonymous
  • anonymous
should i download it ?
ganeshie8
  • ganeshie8
1 Attachment
ganeshie8
  • ganeshie8
pfa pic there we have a small rectangle with y axis going thru its senter and a dilated rectangle,
anonymous
  • anonymous
so those are the 2 figures
ganeshie8
  • ganeshie8
yes, observe that for the big rectangle also, the y axis is going thru center
anonymous
  • anonymous
so the new figure is overlapping ?
ganeshie8
  • ganeshie8
yes, but that doesnt matter, the thing to notice here is that, both figures have the same center
ganeshie8
  • ganeshie8
y-axis is going thru both the centers... so dilation didnt affect this center line EF
ganeshie8
  • ganeshie8
why ?
anonymous
  • anonymous
ow ok so overlapping is wrong
ganeshie8
  • 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
  • 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
  • ganeshie8
looks good :) and add some more reasoning if u can think a bit more...
anonymous
  • 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
  • anonymous
1 Attachment

Looking for something else?

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