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

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

With the being said, i was wondering if within parallel the diagonals bisect the angle which the meet.

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For instance, please describe the link, walk $overlineAC$ bisect $angle BAD$ and also $angle DCB$?

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

Thanks, guys!


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edited might 21 "20 at 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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$egingroup$ Yes however not a common parallelogram, only in a square, rhombus and also kite. $endgroup$
–user312097
Jun 3 "16 in ~ 17:11
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The diagonals bisect angles just if the sides 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 $ riangle BAC$ is isosceles through $AB=BC$.

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


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answer Jun 3 "16 at 16:53
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KalElKalEl
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Nope the doesn"t...We can prove it using congruency triangle.U can see that vertically opposite angles are equal.Not the diagonal line bisect angle


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