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# Is the quadrilateral ABCD a parallelogram? 1. AB=BC 2.

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Manager
Joined: 09 May 2006
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03 Jun 2006, 09:50
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Is the quadrilateral ABCD a parallelogram?

1. AB=BC

2. BC=CD=DA

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Manager
Joined: 19 Apr 2006
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03 Jun 2006, 10:20
this is a Yes or No question...

We know that ABCD is a Quadrilateral but that is all the information we get. But the definition of a Quadrilateral is a four sided polynomial, so we can not assume it is square or a rectangular.

1) not sufficient because it only tells us that two sides are equal to each other. A and D out.

2) not sufficient because it only tells us that three sides are equal to each other. What about AB? B is out...

Left with C or E...

By combining both, I still feel that there is still not enough information because we know that the lengths are the same, but how about the angles? or are any of the lines parallel from each other. I can draw a shape of a bow tie with all lines to be the same length and it will not be considered a parallelogram... am I looking at this problem in weird way? comments anyone?

I go with E

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Director
Joined: 13 Nov 2003
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03 Jun 2006, 10:34
IMO a quadrilateral with 4 equal sides should be paralelogram.
SO C
IF you split the quadrilatteral in 2 triangles at the short or the long diagonals, then the cross angles are equal which means that sides are parallel

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VP
Joined: 21 Sep 2003
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03 Jun 2006, 10:41
Yep agree iwth BG:

Here are 5 ways to conclude if a quadrilateral is a parallelogram:
1. Opposite sides are PARALLEL (AB||CD & AD||BC)
2. Opposite sides are EQUAL (AB =CD and AD=BC)
3. Two sides are EQUAL and PARALLEL (AB = CD and AB is parallel to CD)
4. Opposite angles are EQUAL (ABC = ADC & BAD = BCD)
5. Diagonals BISECT each other.
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Manager
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03 Jun 2006, 11:18
giddi77 wrote:
Yep agree iwth BG:

Here are 5 ways to conclude if a quadrilateral is a parallelogram:
1. Opposite sides are PARALLEL (AB||CD & AD||BC)
2. Opposite sides are EQUAL (AB =CD and AD=BC)
3. Two sides are EQUAL and PARALLEL (AB = CD and AB is parallel to CD)
4. Opposite angles are EQUAL (ABC = ADC & BAD = BCD)
5. Diagonals BISECT each other.

Correct answer is C. Great tip giddi77!

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Manager
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03 Jun 2006, 20:42
Thanks for the clarification giddi.

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03 Jun 2006, 20:42
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