Parallelogram DS

[goelmohit2002]

Is ABCD parallelogram ?
1) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
2) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

[Ben Ku]

Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

[goelmohit2002]

one of my friends asked me this question....not sure what is the original source.

[nimish.tiwari]

Is ABCD parallelogram ?
1) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
2) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

From (1): Consider any quadrilateral ABCD in which opposite sides are equal. This can only happen when these sides are parallel as well. Hence, ABCD is a parallelogram. Hence, this is sufficient. (Note: I do not recall any theorem as such for this, however, i have approached this by visualization of such a figure).

From (2): That's the property of parallelograms - opposite sides are parallel. Hence, 2 is also sufficient.

Hence, my opinion is that answer should be (D), unless I haven't made any major blunders in visualization :).

[aboinpally]

I think the answer is C.
I might have come across this question in one of (MGMAT) strategy guides probably geometry.

1) Just saying opposite sides are equal does not prove it to be a parallelogram.
2) Just saying opposite sides are parallel does not prove it to be a parallelogram.
1) & 2) according to definition of a parallelogram any quadrilateral that has opposite sides parallel and equal is a parallelogram. Therefore C.

Square, Rectangle, Rhombus are parallelograms.

[hisabness]

one of my friends asked me this question....not sure what is the original source.

This is a Manhattan GMAT question...

[gorav.s]

changed to C

[goelnikhils]

I think answer should be 'C'.

Refer to OG 11 please for definition of parallelogram. It says a parallelogram is a Quadilateral with opp sides as equal and parallel.

Rectangle/Square & Rhombus are all parallelograms that have opp sides as equal and parallel.

Also parallelogram has following properties also
- Opp angles are equal
- Adjacent angles sum up to 180 degree

In any parallelogram has one angle as 90 degree then for sure it is a rectangle .

[gorav.s]

i agree ,will correct my mistake

with a only or b only
it cab ce a trapezoid with opposite sides parallel , and a rhombus with opposite sides equal

asswer should be C

[Ben Ku]

By definition, a parallelogram is a quadrilateral where both pairs of opposite sites are parallel. Statement (2) states this fact.

Because (1) describes a quadrilateral where both pairs of opposite sites are equal, it is a also a parallelogram. Statement (1) is sufficient.

The answer here is (D).

If you are given a quadrilateral, you can show they're parallelograms in any of the following ways:
(1) BOTH pairs of opposite sides are congruent.
(2) BOTH pairs of opposite sides are parallel.
(3) BOTH pairs of opposite angles are congruent.
(4) ALL four sides have equal length (this is same as (1)); this parallelogram is a rhombus.
(5) ALL four angles have the same measure (this is the same as (3)); this parallelogram is a rectangle.
(6) The diagonals of the quadrilateral bisect each other (they cut each other in half).
(7) ONE pair of opposite sides are BOTH parallel and congruent.

Hope that helps.