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Is quadrilateral ABCD a parallelogram?

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Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 19 Nov 2014, 00:31
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A
B
C
D
E

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  55% (hard)

Question Stats:

49% (01:11) correct 51% (01:29) wrong based on 164 sessions

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Is quadrilateral ABCD a parallelogram?

(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC
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Re: Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 19 Nov 2014, 10:40
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anant07 wrote:
Is quadrilateral ABCD a parallelogram?

(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC


In order to prove that a quadrilateral is a parallelogram at least one of the following should be true:--
1. Two pairs of opposite sides are equal or parallel
2. One pair of opposite side is equal and parallel
3. Both the pairs of opposites angles are equal
4. Diagonals bisect each other

Considering the problem
STAT1 : Area of Triangle ABC = Area of Triangle ACD
From this we just know that there is a diagonal AC and on it's two sides there are two triangles which have same area. IF we would have given that the base of these two triangles are equal and parallel then we could prove that the quadrilateral is a parallelogram. But not we can't.

STAT2: It just tells us that two adjacent are equal. Which is of no use to us.

Combining these two also doesn't give us any concrete information to prove that the figure is a parallelogram.

So, INSUFFICIENT
Hence, Answer will be E

Hope it helps!
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Re: Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 19 Nov 2014, 11:28
We just need to find out if ABCD has 2 sets of parallel sides since we know that it is a quadrilateral.

statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.

statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides

Together, ABCD must be either a square or a rhombus, both of which are paralellograms.

Answer C!
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Re: Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 20 Nov 2014, 09:15
DangerPenguin wrote:
We just need to find out if ABCD has 2 sets of parallel sides since we know that it is a quadrilateral.

statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.

statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides

Together, ABCD must be either a square or a rhombus, both of which are paralellograms.

Answer C!


Notice that the correct answer is E, not C. Try again.
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Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 28 Jan 2018, 08:49
DangerPenguin wrote:
We just need to find out if ABCD has 2 sets of parallel sides since we know that it is a quadrilateral.

statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.

statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides

Together, ABCD must be either a square or a rhombus, both of which are paralellograms.

Answer C!


hi

Still the quadrilateral can be a isosceles trapezoid

so the answer is E
thanks
:cool:
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Re: Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 19 Feb 2019, 22:59
BrushMyQuant wrote:
anant07 wrote:
Is quadrilateral ABCD a parallelogram?

(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC


In order to prove that a quadrilateral is a parallelogram at least one of the following should be true:--
1. Two pairs of opposite sides are equal or parallel
2. One pair of opposite side is equal and parallel
3. Both the pairs of opposites angles are equal
4. Diagonals bisect each other

Considering the problem
STAT1 : Area of Triangle ABC = Area of Triangle ACD
From this we just know that there is a diagonal AC and on it's two sides there are two triangles which have same area. IF we would have given that the base of these two triangles are equal and parallel then we could prove that the quadrilateral is a parallelogram. But not we can't.

STAT2: It just tells us that two adjacent are equal. Which is of no use to us.

Combining these two also doesn't give us any concrete information to prove that the figure is a parallelogram.

So, INSUFFICIENT
Hence, Answer will be E

Hope it helps!


hi , from st(2) , if adjacent sides are equal , can't we say its not a parallelogram , as in a parallelogram oppo. sides are equal
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Re: Is quadrilateral ABCD a parallelogram?  [#permalink]

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New post 20 Feb 2019, 04:44
Just draw two triangles merged into a figure like boomerang and there are 2 triangles with same area and AD=DC sides... and a parallelogram. Thus, answer is E, its too obvious that C is a trap answer. :)
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Re: Is quadrilateral ABCD a parallelogram?   [#permalink] 20 Feb 2019, 04:44
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