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# Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD

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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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25 Jun 2018, 09:59
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23% (01:44) correct 77% (01:32) wrong based on 61 sessions

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Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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25 Jun 2018, 10:55
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.

statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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27 Jun 2018, 11:41
Can somebody please give an explanation to the question? The OA is C
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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27 Jun 2018, 12:42
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.

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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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28 Jun 2018, 05:42
4
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.

statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

DONT FORGET TO KUDOS

Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure
Attachments

quad-rectangle.png [ 10.14 KiB | Viewed 933 times ]

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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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28 Jun 2018, 07:19
chetan2u wrote:
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.

statement 1 is insufficient alone, as the quadrilateral can be a square as well as a rectangle ( as per given info)
statement 2 is also insufficient alone as the quadrilateral can be a square as well as a rectangle ( as per given info)

combining statement will also not help in solving the problem as both square and rectangle satisfy the condition.

Hence E

DONT FORGET TO KUDOS

Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure

Nice explanation, but I want to know why the combination of the statement A and B cannot be a rohmbus. (it has bisecting diagonals and for that matter statement 1 is also true for a rohmbus.
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Posts: 8616
Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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28 Jun 2018, 08:06
chetan2u wrote:
amanvermagmat wrote:
Is the quadrilateral ABCD a rectangle?

(1) Mid points of AB, BC, CD and AD are E, F, G and H respectively. Quadrilateral EFGH is a rhombus.

(2) Diagonals of quadrilateral ABCD bisect each other.

Square is also a rectangle..
so if ABCD is a square, it means it is a rectangle.
ofcourse vice versa may not be true

also statement I will be true for an isosceles trapezium too along with rectangle..
and statement II will also be true for rhombus along with rectangle and any parallelogram for that matter

combined
it will be a rectangle ..
see attached figure

Nice explanation, but I want to know why the combination of the statement A and B cannot be a rohmbus. (it has bisecting diagonals and for that matter statement 1 is also true for a rohmbus.

Incase you have a rhombus which has all sides equal but angles are not 90..
If you join the midpoints of side of this rhombus, the parallelogram so formed will not be a rhombus as all four sides will not be equal. Only opposite sides will be equal
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD  [#permalink]

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07 Aug 2019, 20:15
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Re: Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD   [#permalink] 07 Aug 2019, 20:15