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# ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?

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Manager
Joined: 15 Dec 2015
Posts: 114
GMAT 1: 680 Q49 V34
GPA: 4
WE: Information Technology (Computer Software)
ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?  [#permalink]

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31 Jul 2017, 00:58
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Difficulty:

55% (hard)

Question Stats:

52% (01:15) correct 48% (01:20) wrong based on 58 sessions

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ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?

1. Angle B+Angle D =180°
2. The quadrilateral ABCD is a parallelogram.
Manager
Joined: 15 Dec 2015
Posts: 114
GMAT 1: 680 Q49 V34
GPA: 4
WE: Information Technology (Computer Software)
Re: ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?  [#permalink]

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31 Jul 2017, 01:01
2
DH99 wrote:
ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?

1. Angle B+Angle D =180°
2. The quadrilateral ABCD is a parallelogram.

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Math Expert
Joined: 02 Aug 2009
Posts: 8326
ABCD is a quadrilateral in which angle A = 90°. Is ABCD a rectangle?  [#permalink]

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28 Nov 2019, 07:24
JiddiHuMain wrote:
ABCD is a quadrilateral in which angle A = 90°. Is ABCD a rectangle?

(1) Angle B + Angle D = 180 degrees.

(2) The quadrilateral ABCD is a parallelogram.

(1) $$\angle B + \angle D = 180°$$.
So, $$\angle A + \angle C = 90°$$, but B and D could be anything totaling to 180.

(2) The quadrilateral ABCD is a parallelogram.
If ABCD is a parallelogram, opposite angles are equal, so $$\angle A = \angle C = 90°$$.
$$\angle B = \angle D$$, and their sum should be 180, so $$\angle B = \angle D=90°$$
Thus ABCD is a rectangle for sure, and if its sides are equal, it may even be square.
Suff

B
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ABCD is a quadrilateral in which angle A = 90°. Is ABCD a rectangle?   [#permalink] 28 Nov 2019, 07:24
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