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805+ (Hard)|   Geometry|      
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amanvermagmat
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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 25 Jun 2018, 10:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

26% (01:49) correct 74% (01:39) wrong based on 116 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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C
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ReadyPlayerOne
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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 25 Jun 2018, 11:55
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amanvermagmat
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.
Show more

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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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 27 Jun 2018, 12:41
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Can somebody please give an explanation to the question? The OA is C
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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 27 Jun 2018, 13:42
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amanvermagmat
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.
Show more


Amanverma Kindly give the answer with explanation. I think there is some more info needed for answer choice C to be OA
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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 28 Jun 2018, 06:42
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amanvermagmat
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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Show more

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
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quad-rectangle.png
quad-rectangle.png [ 10.14 KiB | Viewed 3173 times ]

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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 28 Jun 2018, 08:19
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chetan2u
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amanvermagmat
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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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
Show more











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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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 28 Jun 2018, 09:06
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ReadyPlayerOne
chetan2u
amanvermagmat
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.
Show more


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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Is the quadrilateral ABCD a rectangle? (1) Mid points of AB, BC, CD 12 Aug 2023, 11:29
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