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

You are watching: Do diagonals bisect angles in a parallelogram

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

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

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

Thanks, guys!


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edited might 21 "20 at 10:41
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amWhy
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inquiry Jun 3 "16 at 16:45
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RidhwaanRidhwaan
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$egingroup$ Yes however not a regular parallelogram, just in a square, rhombus and kite. $endgroup$
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The diagonals bisect angles only if the sides are all of equal length.

Proof -

Assume the the diagonals undoubtedly bisect angles.

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

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

So $angle BCE = angle EAB$, thus $ riangle BAC$ is isosceles with $AB=BC$.

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


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


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