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

Question

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

(1) AB = CD
(2) AD = BC

shilpiruchi · Answer

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.

lucasITA · Answer

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?

ConnectTheDots · Answer

B is sufficient. Please refer the diagram.

lucasITA · Answer

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? :?:

bleajor · Answer

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

(1) AB = CD
(2) AD = BC
-------------------------

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.

Bunuel · Answer

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.

reto · Answer

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?

ENGRTOMBA2018 · Answer

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.

acegmat123 · Answer

Statement 1:

Can be trapezoid or parallelogram

Insufficient

Statement 1:

Must be a parallelogram

Sufficient

B

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Joc456 · Answer

One of the properties of a parallelogram is one set of parallel lines that are equal. B

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

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