Is quadrilateral ABCD a rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD
A rhombus is a quadrilateral with all its sides equal to each other.
Imagine that the point where the bisectors meet is called X.
Then, BX = DX and AX = CX.
Using the Pythagorean Theorem you could imagine getting the hypotenuse of sides BX and CX.
Since AX = CX, then the hypotenuse of BX and AX is also as long as the previous.
As you could imagine, all the hypotenuse formed are equal, thus forming equal 4 sides. Hence, a rhombus.
All sides are equal.