Is quadrilateral ABCD a parallelogram? (1) AC = BD

Question

Is quadrilateral ABCD a parallelogram?

(1) AC = BD
(2) AC and BD bisect each other.

deepudiscover · Answer

I think the answer should be B.
Diagonal bisecting each other proves parallelogram by using SAS(Side, Angle, Side) congruency.
Experts please help  chetan2u

chetan2u · Answer

Hi..

I agree with you. diagonals bisecting each other is a SUFFICIENT condition for a Quadrilateral to be a PARALLELOGRAM..
 DH99 , pl relook in the Q. either there is a typing error(  something else instead of Quadrilateral ) or OA is marked incorrectly.

vivek2k70 · Answer

It can be rhombus or square as well

chetan2u · Answer

Hi...
parallelogram is the BASE form of all these..
rhombus, square or rectangle .. all of them are TYPES of PARALLELOGRAM..

DHAR · Answer

Hi,

The OA is marked as E.This is how I solved it I am not sure if it is correct.Please evaluate:
Statement1>> Can be a Isoscelles Trapezium,Square/Rectangle.(Isoscelles Trapezium is a not a ||gm but a quadrilateral)
Statement1>> Can be a Isoscelles Trapezium, Square/Rectangle.

1+2>> Isoscelles Trapezium or Rectangle .  E

chetan2u · Answer

OA is wrong then. It has to be B
Isosceles trapezium - its diagonals do not bisect each other. they are equal.

imyuva · Answer

quadrilateral.jpg It can also be in this shape.. here AC = BD and AC and BD bisects.. this is not a parallelogram. Sent from my KIW-L22 using GMAT Club Forum mobile app

darn · Answer

These diagonals will not bisect each other in this case. You can go ahead and draw an isosceles trapezium to scale and then measure to see if the diagonals bisect each other.. You will realize that they will not! Only in a parallelogram can this happen.

PyjamaScientist · Answer

Property of a parallelogram: Diagonals of a parallelogram bisect each other . Statement 2 states that explicitly and thus is sufficient.
Statement 1 is insufficient as diagonals can be equal even in the case of a trapezium which is not a parallelogram, thus this condition alone is not sufficient.
Option (B).

Asha7 · Answer

Property of a parallelogram: Diagonals of a parallelogram bisect each other. - But this also is the property of the Rectangle?
And Rectangle is also a quadrilateral.
I think the answer is option E.

Kushchokhani · Answer

Asha7

All rectangles are parallelograms.

Bunuel

I understand that difficulty level of a question is determined basis % of students who marks correctly. However, this is a property question and don't think should be classified as 700-level. There should be some more parameters to classify difficulty level of a ques.

gmatwhiz

Your concept file in FT states that diagonals of a trapezium are not equal. However, as per this ques OA, it seems that they may be equal.

bumpbot · Answer

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Is quadrilateral ABCD a parallelogram? (1) AC = BD

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