Opposite sides space parallel and equal in length.Opposite angles room equal.Adjacent angles include up come 180 degrees therefore nearby angles are supplementary angles. (Their amount equal to 180 degrees.) The diagonals of a parallelogram bisect every other.

You are watching: Do diagonals bisect each other in a parallelogram

With that being said, ns was wondering if within parallel the diagonals bisect the angles which the meet.

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For instance, please describe the link, does $\overlineAC$ bisect $\angle BAD$ and $\angle DCB$?

If castle diagonals do undoubtedly bisect the angles which they meet, can you please, in layman"s terms, show your proof?

Thanks, guys!


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edited may 21 "20 in ~ 10:41
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amWhy
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asked Jun 3 "16 in ~ 16:45
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RidhwaanRidhwaan
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$\begingroup$ Yes however not a regular parallelogram, only in a square, rhombus and also kite. $\endgroup$
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The diagonals bisect angles just if the political parties are all of equal length.

Proof -

Assume that the diagonals undoubtedly bisect angles.

Then $\angle BCE=\angle ECD$ in her diagram.

Also $\angle ECD=\angle EAB$ because $AB \| DC$.

So $\angle BCE = \angle EAB$, hence $\triangle BAC$ is isosceles with $AB=BC$.

Similar arguments likewise prove equality of various other sides, $BC=CD$ and also $CD=DA$.


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answered Jun 3 "16 in ~ 16:53
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KalElKalEl
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Nope it doesn"t...We have the right to prove it utilizing congruency triangle.U have the right to see the vertically opposite angles space equal.Not the diagonal bisect angle


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answered may 15 "19 in ~ 5:11
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HEPIN RAJESHBHAI SAVALIYAHEPIN RAJESHBHAI SAVALIYA
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