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Is quadrilateral ABCD a rectangle?

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Joined: 03 May 2014
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Re: Is quadrilateral ABCD a rectangle? [#permalink]

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New post 10 Jul 2017, 10:22
Bunuel wrote:
700byforce wrote:
Can anyone articulate how we deduce from the fact that, if one angle of a parallelogram is 90 degrees and the opposite angle is equal, how do we come to the conclusion that the other pair of opposite angles are also equal to 90 degrees?


Useful property: the adjacent angles of a parallelogram are supplementary (supplementary angles are two angles that add up to 180°). So, if angle B is 90°, then A and C must also be 90° to add up to 180.

Hope it helps.


Many thanks. Very crisp explanation.

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Re: Is quadrilateral ABCD a rectangle? [#permalink]

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New post 13 Sep 2017, 04:24
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praveenboddu wrote:
319 wrote:
Is quadrilateral ABCD a rectangle?
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Why is the answer C? and not E? It can be a square and not a rectangle.


I guess square is a special rectangle. I am not sure whether we can consider like this. Thoughts



All squares are rectangles, so the answer would still be YES.hence C

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Location: India
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GPA: 3.32
WE: Programming (Computer Software)
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Re: Is quadrilateral ABCD a rectangle? [#permalink]

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New post 13 Sep 2017, 04:26
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Edofarmer wrote:
Can anyone articulate how we deduce from the fact that, if one angle of a parallelogram is 90 degrees and the opposite angle is equal, how do we come to the conclusion that the other pair of opposite angles are also equal to 90 degrees?


the adjacent angles of a parallelogram add up to 180. So, if angle B is 90°, then A and C must also be 90° to add up to 180.

Kudos [?]: 27 [0], given: 28

Re: Is quadrilateral ABCD a rectangle?   [#permalink] 13 Sep 2017, 04:26

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