Question 1165628
.
Given: AB= DC
prove: AC= DB
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The problem formulation in the post is FATALLY INCOMPLETE,
and therefore the problem can not be solved properly.


The logic and the reasoning in the post by @CPhill are irrelevant 
to the possible case. @CPhill starts from consideration of a kite shape,
which is 100% not relevant to the given equalities.


If this relates to quadrilaterals on the plane, then only two cases
can be relevant: (a) parallelograms, and (b) isosceles trapezoids.


But then the problem's description must provide relevant conditions 
for such a quadrilateral to be a parallelogram or an isosceles trapezoid.


Without it, the problem is the same absurdist non-sensical creation
as a two-leg horse from the story about the baron Munchausen
and can exist only in sick imagination or in tales for children to make them laugh.



Posting such incomplete defective "problems" to this forum is unacceptable hooliganism.



The way how @CPhill reacts to such absurdist problems, is a hooliganism in degree 7 (seven).

He piles nonsense on top of other nonsense.