gijoedude wrote:

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.

1.

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.

SUFFICIENT.

2.

All sides are equal.

SUFFICIENT.

Answer: D

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