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# Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.

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Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.  [#permalink]

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02 Jun 2015, 12:39
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5
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Difficulty:

25% (medium)

Question Stats:

67% (00:44) correct 33% (00:49) wrong based on 117 sessions

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(1) BC and DA are parallel.

(2) BC and DA are equal in length.

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Re: Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.  [#permalink]

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05 Jun 2015, 04:19
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1
Parallelogram is defined as a quadrilateral with 2 pairs of parallel sides.

(1) BC and DA are parallel.
This can be both, parallelogram or not. See rectangle and trapezoid, both meet the requirements. Insufficient.

(2) BC and DA are equal in length.
Same as in Statement 1. Insufficient.

(1) & (2) Together.
If two sides are parallel and equal, two remaining sides will have the same properties. Sufficient.
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Re: Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.  [#permalink]

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05 Jun 2015, 04:36
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reto wrote:

(1) BC and DA are parallel.

(2) BC and DA are equal in length.

Questions: Is quadrilateral ABCD a parallelogram?

Statement 1: BC and DA are parallel.

With two opposite sides paralle the Quadrilateral could be a Parallelogram or a Trapezium

Hence, NOT SUFFICIENT

Statement 2: BC and DA are equal in length

With Two opposite Sides equal a Quadrilateral could be a Parallelogram or an Isosceles Trapezium with equal un-parallel legs

Hence, NOT SUFFICIENT

Combining the two statements:

With two opposite sides equal and Parallel, The quadrilateral is bound to be a Parallelogram

Hence, SUFFICIENT

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Re: Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.  [#permalink]

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11 Sep 2019, 18:26
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Re: Is quadrilateral ABCD a parallelogram? (1) BC and DA are parallel.   [#permalink] 11 Sep 2019, 18:26
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