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# In the quadrilateral ABCD, side AD is parallel to side BC.

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Intern
Joined: 21 Aug 2011
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Updated on: 07 Sep 2013, 09:19
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Difficulty:

55% (hard)

Question Stats:

52% (01:21) correct 48% (01:11) wrong based on 240 sessions

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In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD

Originally posted by siddharthvaid on 25 Aug 2011, 13:42.
Last edited by Bunuel on 07 Sep 2013, 09:19, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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25 Aug 2011, 14:21
1
siddharthvaid wrote:
Q) In Quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

a) AB=CD

Data sufficiency?

Are you sure your ans is correct?

I think B (Statement B alone) should be correct as it always gives an ans Yes while statement A gives sometimes yes sometimes no.

cauz-

If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram.
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07 Sep 2013, 05:30
I've found the same answer in Kaplan CAT 5. My answer is E, but the OA is B. I don't understand. What is the difference between answer A and B (there isn't any picture, so for example i can name the same side as AB or BC). am i wrong?
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07 Sep 2013, 05:41
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1
B is sufficient. Please refer the diagram.
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Parallelogram.jpg [ 22.64 KiB | Viewed 41677 times ]

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07 Sep 2013, 06:01
ConnectTheDots wrote:
B is sufficient. Please refer the diagram.

but is a correct hypothesis that vertex A is the upper vertex on the left?!
can't i chose vertex A as the lower vertex on the left?
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04 Feb 2015, 07:24
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
-------------------------

If AD = BC & AD is parallel to side BC >> I think ABCD could be a square or a parallelogram .

So, I pick E.

--------------------------
Anyone can explain why B is OA.
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04 Feb 2015, 09:11
bleajor wrote:
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD
-------------------------

If AD = BC & AD is parallel to side BC >> I think ABCD could be a square or a parallelogram .

So, I pick E.

--------------------------
Anyone can explain why B is OA.

A square is a special type of a parallelogram, so if a figure is a square, then it's also a parallelogram (but not vise-versa).

Check Polygons chapter of our math book.

Hope it helps.
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11 Aug 2015, 14:00
siddharthvaid wrote:
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD

Is there a systematic approach for such questions? Do you directly start drawing if the question says AD is parallel to BC and then go on from there with Statement 1, Statement 2 etc?
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11 Aug 2015, 14:06
2
reto wrote:
siddharthvaid wrote:
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD

Is there a systematic approach for such questions? Do you directly start drawing if the question says AD is parallel to BC and then go on from there with Statement 1, Statement 2 etc?

You should remember that for a quadrilateral to be a parallelogram , you need to have either 1 pair of equal and parallel sides ((the equal and parallel sides should refer to the SAME pair) or have 2 pairs of parallel sides (they indirectly mean the same thing).

Once you realise this, you see clearly that statement 1 with AD||BC , does not help us in any way.

Statement 2 with AD||BC does give us a "yes" answer on the basis that any quadrilateral with 1 pair of equal and parallel sides (the equal and parallel sides should refer to the SAME pair). This statement is thus sufficient.
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03 Nov 2016, 10:23
SW4 wrote:
In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram?

(1) AB = CD

Statement 1:

Can be trapezoid or parallelogram

Insufficient

Statement 1:

Must be a parallelogram

Sufficient

B

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03 Nov 2016, 11:54
One of the properties of a parallelogram is one set of parallel lines that are equal. B
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23 Aug 2019, 18:37
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Re: In the quadrilateral ABCD, side AD is parallel to side BC.   [#permalink] 23 Aug 2019, 18:37
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