Data Sufficiency

Is ABCD parallelogram ?
a) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
b) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

it is d

b) parallelogram

oops, a) is a parallelogram too. d it is

I also think D shd be the answer....but the definition of Manhattan at the below link seems to be saying = C......not sure why....I guess both alone are sufficient.

https://www.manhattangmat.com/geo-polygons.cfm

Is ABCD parallelogram ?
a) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
b) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

Statement B alone is Suff. but A alone is not.

A can be an isoceles trapezium.

On second thoughts:

Parallelogram"Opposite sides are parallel and equal.

Hence C.

I have a doubt.If the Opposite sides are parallel then they will definitely be equal.It should be B.Am I missing something?

vikram_k51 wrote:Is ABCD parallelogram ?
a) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
b) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

Statement B alone is Suff. but A alone is not.

A can be an isoceles trapezium.

Can you tell what is isoceles trapezium and how does it look like satisfying A ?

goelmohit2002 wrote:

vikram_k51 wrote:Is ABCD parallelogram ?
a) Opposite sides i.e. (AB, CD) and (BC, AD) are equal.
b) Opposite sides i.e. (AB, CD) and (BC, AD) are parallel.

Statement B alone is Suff. but A alone is not.

A can be an isoceles trapezium.

Can you tell what is isoceles trapezium and how does it look like satisfying A ?

Here you go:

https://images.google.com/images?hl=en&r ... e&resnum=4

I stand corrected.The opposite sides are not equal here

Thanks

But...the above figures show only sloping lines equal.....but the opposite parallel lines are unequal.....(option A says both pair of sides are equal)

Also just searched for defintion too.....

https://www.tiscali.co.uk/reference/ency ... 06746.html

it too says that only sloping sides are equal....does not talk about the parallel lines.

isn't it or I am missing something here or there is some special case that is also there ?

goelmohit2002 wrote:I also think D shd be the answer....but the definition of Manhattan at the below link seems to be saying = C......not sure why....I guess both alone are sufficient.

https://www.manhattangmat.com/geo-polygons.cfm

the link doesnt seem to say C.
a parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

if opposite sides are are to be equal, they would be parallel as well
if opposite sides are to be parallel, they would be equal as well

so either statement is sufficient

Guys if opposite sides are parallel then it can be shown that they will be equal, so condition B should suffice.

See the following construction:

---------------------------


---------------------------

If you connect them the alternate angle will be equal. connect both the diagonal you will get two angles are equal so all angles will be equal..

now come to following fact, if we want to join these two ends by parallel sides they needs to be equal.

Combining the above two the two angles equal and a side each equal, means the two half will be congruent.

Means corresponding sides will be equal and so a parrellelogram...

scoobydooby wrote:

goelmohit2002 wrote:I also think D shd be the answer....but the definition of Manhattan at the below link seems to be saying = C......not sure why....I guess both alone are sufficient.

https://www.manhattangmat.com/geo-polygons.cfm

the link doesnt seem to say C.
a parallelogram is a quadrilateral in which the opposite sides are parallel and equal.

if opposite sides are are to be equal, they would be parallel as well
if opposite sides are to be parallel, they would be equal as well

so either statement is sufficient

Thanks Scooby. I also think so...can we interpret the Manhattan statement as follows:

Given By Manhattan:
===============
Parallelogram: A four-sided closed shape composed of straight lines in which the opposite sides are equal and the opposite angles are equal.

Correct one:
=========
i.e. if either of the following two are given then it is parallelogram.

#1
Parallelogram: A four-sided closed shape composed of straight lines in which the opposite sides are equal.

OR
#2
Parallelogram: A four-sided closed shape composed of straight lines in which the opposite angles are equal.

maihuna wrote:Guys if opposite sides are parallel then it can be shown that they will be equal, so condition B should suffice.

See the following construction:

---------------------------


---------------------------

If you connect them the alternate angle will be equal. connect both the diagonal you will get two angles are equal so all angles will be equal..

now come to following fact, if we want to join these two ends by parallel sides they needs to be equal.

Combining the above two the two angles equal and a side each equal, means the two half will be congruent.

Means corresponding sides will be equal and so a parrellelogram...

It should be D.

If the opposite sides are equal they will def be parallel and if they are parallel they will also be equal.

vikram_k51 wrote:

maihuna wrote:Guys if opposite sides are parallel then it can be shown that they will be equal, so condition B should suffice.

See the following construction:

---------------------------


---------------------------

If you connect them the alternate angle will be equal. connect both the diagonal you will get two angles are equal so all angles will be equal..

now come to following fact, if we want to join these two ends by parallel sides they needs to be equal.

Combining the above two the two angles equal and a side each equal, means the two half will be congruent.

Means corresponding sides will be equal and so a parrellelogram...

It should be D.

If the opposite sides are equal they will def be parallel and if they are parallel they will also be equal.

In the trapezium, the non parallel sides can be equal. It cannot be D.

It should be C

Guys,

If it is C, that means that the opposite sides are equal length and parallel to one another.

These two properties hold for a rectangle as well. The choice should be E. The difference between the two is that rectangles have 90 degree angles while a parallelogram's interior angles add up to 360 degrees.

I go with E