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.

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

amWhy

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inquiry Jun 3 "16 at 16:45

RidhwaanRidhwaan

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$endgroup$

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$egingroup$ Yes however not a regular parallelogram, just in a square, rhombus and kite. $endgroup$

–user312097

Jun 3 "16 at 17:11

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## 2 answers 2

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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

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

HEPIN RAJESHBHAI SAVALIYAHEPIN RAJESHBHAI SAVALIYA

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