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# Is ABCD a square? (1) AB is parallel to CD (2) ABCD is an equilateral

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Math Expert
Joined: 02 Sep 2009
Posts: 52295
Is ABCD a square? (1) AB is parallel to CD (2) ABCD is an equilateral  [#permalink]

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08 Feb 2018, 04:51
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:51) correct 23% (00:56) wrong based on 59 sessions

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Is ABCD a square?

(1) AB is parallel to CD .

(2) BCD is an equilateral triangle.

Attachment:

2018-02-08_1649.png [ 5.51 KiB | Viewed 803 times ]

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Math Expert
Joined: 02 Sep 2009
Posts: 52295
Re: Is ABCD a square? (1) AB is parallel to CD (2) ABCD is an equilateral  [#permalink]

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08 Feb 2018, 04:53
Bunuel wrote:

Is ABCD a square?

(1) AB is parallel to CD .

(2) BCD is an equilateral triangle.

Attachment:
2018-02-08_1649.png

Check Properties of Polygons Questions from our Special Questions Directory.
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Re: Is ABCD a square? (1) AB is parallel to CD (2) ABCD is an equilateral  [#permalink]

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08 Feb 2018, 07:23
1
Bunuel wrote:

Is ABCD a square?

(1) AB is parallel to CD .

(2) BCD is an equilateral triangle.

Attachment:
2018-02-08_1649.png

Statement 1

AB is parallel to CD. So at least this quadrilateral is a trapezoid. But we don't know about other two sides. So we don't even know if this is a parallelogram or not, we surely cannot determine whether its a square or not. So not sufficient.

Statement 2

Each angle of an equilateral triangle is 60 degrees, so angle BCD is 60 degrees, but each of the four angles of a square must be 90 degrees. We can thus conclude that quadrilateral ABCD cannot be a square, so this gives us NO as an answer to the question asked. Sufficient.

Re: Is ABCD a square? (1) AB is parallel to CD (2) ABCD is an equilateral &nbs [#permalink] 08 Feb 2018, 07:23
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