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So, from the given data figure can be rhombus or sqare? and logically they are different figures. I have come across lots of rectangle and sqare problems causing same type of confusion but in those questions we look for exact specs.
Square is a very special quadrilateral. It can be seen as a special type of parallelogram, a special rectangle, and a special rhombus.
As for crossed quadrilaterals, I do not believe that it is possible that all of its sides are equal. Let's use the shape in the link you provided, ADBC. If AC=AD then angle ACD=angle ADC. If BC=BD, then angle BCD=angle BDC. However we also know that angle ACD < angle BCD and angle ADC > angle BDC. You can see that if the two angles in the right hand side are equal, then the angles in the left hand side can NOT be equal. _________________
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