Why the answer is D

[joshi.komal]

Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD


I am not sure why stmt 2 is sufficient... Can anyone explain

Thanks
Komal

[sankruth]

St 1: SUFF
If diagonals are perpendicular bisectors of each other then fugure is a Square or Rhombus.

St2 : SUFF
If 4 sides are equal, then figure must be a square or rhombus. Square is Rhombus where both diagonals have equal length and are perpendicular bisectors of each other

So, D. Hope that helps!

[Stuart@KaplanGMAT]

A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square is a special kind of rectangle).

So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.

[preciousrain7]

A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square/rhombus is a special kind of rectangle).

So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.

Stuart,

is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?

Sonia

[Stuart@KaplanGMAT]

A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square is a special kind of rectangle).

So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.

Stuart,

is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?

Sonia

Not quite. Here's what we can say:

A square IS a rhombus.
A rhombus MAY BE a square.

A square IS a rectangle.
A rectangle MAY BE a square.

(I misstated the rhombus/rectangle relationship in my original post and have edited it - a rhombus isn't a rectangle, since all rectangles have 4 * 90 degree angles; a rectangle can be a rhombus, but only if it's also a square.)

[preciousrain7]

Stuart,

is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?

Sonia

Not quite. Here's what we can say:

A square IS a rhombus.
A rhombus MAY BE a square.

A square IS a rectangle.
A rectangle MAY BE a square.

(I misstated the rhombus/rectangle relationship in my original post and have edited it - a rhombus isn't a rectangle, since all rectangles have 4 * 90 degree angles; a rectangle can be a rhombus, but only if it's also a square.)[/quote]

Thank you.