Opposite sides space parallel and equal in length.Opposite angles room equal.Adjacent angles add up to 180 levels therefore nearby angles room supplementary angles. (Their sum equal come 180 degrees.) The diagonals that a parallelogram bisect each other.

You are watching: Do the diagonals of a rhombus bisect the angles

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

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

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

Thanks, guys!


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edited may 21 \"20 at 10:41
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amWhy
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request Jun 3 \"16 in ~ 16:45
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RidhwaanRidhwaan
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$\\begingroup$ Yes yet not a typical parallelogram, only in a square, rhombus and also kite. $\\endgroup$
–user312097
Jun 3 \"16 in ~ 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 that the diagonals certainly bisect angles.

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

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

So $\\angle BCE = \\angle EAB$, thus $\\triangle BAC$ is isosceles through $AB=BC$.

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


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


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