Does this theorem has been proved yet?

Question

I am having a little trouble to prove an hypothesis about Euclidean geometry, This happen because I am using an theorem about the theme that I don't know if is true, can anyone help me? Here is the fount of my problems:

If we take four distinct points, 'A', 'B', 'C' and 'D', being AB with an equal length of CD, the perpendicular bisector of AD is the same of BC.

edit1: I've forgot to say that $AB//CD$

lhf · Answer 1 · 2017-08-18T14:56:13.133

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False.

Consider $A=(0,1), B=(2,0), C=(3,0), D=(1,1)$

edited Aug 18 '17 at 14:56

answered Aug 18 '17 at 12:05

lhf

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i've forgot to say that AB // CD, sorry... – sasinhe Aug 18 '17 at 14:37
but thanks anyway – sasinhe Aug 18 '17 at 14:38

Somos · Answer 2 · 2017-08-18T17:33:13.553

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What you have is a parallelogram and the diagonals bisect each other. If the four points are collinear then the perpendicular bisectors are the same. Otherwise they are different.

edited Aug 18 '17 at 17:33

answered Aug 18 '17 at 17:22

Somos

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so, if I take an parallelogram and take the Perpendicular bisector of his diagonals, will they be on the same point? – sasinhe Aug 18 '17 at 17:29
Yes. All the points are on the same line and the two bisectors are the same points, and so is the perpendicular bisectors. – Somos Aug 18 '17 at 17:32
ok, that helps, thank you. – sasinhe Aug 18 '17 at 17:33

Does this theorem has been proved yet?

2 Answers2