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

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

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New post 31 Jul 2017, 00:58
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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.
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Joined: 15 Dec 2015
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Re: ABCD is a quadrilateral in which angle A is 90°.Is ABCD a rectangle?  [#permalink]

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New post 31 Jul 2017, 01:01
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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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ABCD is a quadrilateral in which angle A = 90°. Is ABCD a rectangle?  [#permalink]

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New post 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.


Firstly please search before posting..

(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

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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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