Parallogram or rectangle or square or rhombus ????

[aru4912]

In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

 

(1) PS = QR

 

(2) PQ = RS

 

Friends, my answer is different from the OA. I dont understand the concept behind the OA. Please help.

 

Thanks,

Arun B

[cognos]

As far as iam concerned

Both the options taken together would be sufficient.

 

All the others (Rhombus,SQUARE,RECTANGLE ) are special forms of a parallelogram.

 

Guys please let me know if iam wrong.

 

Bythe way what is the answer ARUN....

[ken_english]

C for me too

[givemeanid]

I think its D

[hasnathullah]

PQRS cannot be a parallelogram only when PS not equal to QR

 

the two choices clearly prove that ps = qr

 

hence it is d

[abhijit_s_2000]

IMO D.

However it is better to understand a rule of quadiletral.

 

If a line (transversal) intercepts two parallel lines it creates angles. So if another intersects the parallel lines and leaves an intercept. If the two intercepts are equal, the angles created by them with the parallel lines would be equal, hence the two lines would be parallel. Using this principle we can ascertain that PQ = RS, PQ is parallel to RS and it is a parallelogram

 

2) Now for the first condition, if PS parallel to QR, draw a diagonal and two traingles created will be similar to each other using SAS test. Hence PQ is parallel to RS.

 

Hope this helps.

[ken_english]

sorry guys I agree it better be D..I don' know what I was thinking !!

[kikipooh]

I picked C first but now I understand the correct answer is D. Thank you.

[lena741]

I think it should be A:

Statement 2 describes an isosceles trapezoid which is not a parallelogram.

[gmatter007]

Yes

the ans shud be a

[saberman3000]

Ans is A in my opinion

 

Given, PS || QR

 

[1] PS = QR is sufficient. Since opposite sides are || AND equal, it is a sufficient condition to be a paralleogram. The resulting figure could be a square, rhombus or a rectangle, but still is a parallelogram.

 

[2] PQ = RS is not sufficient. Although it still forms a quadrilateral, it can form a trapezoid which is NOT a parallelogram.

 

Whats the OA?

[digvijayrajan]

it should be a

[digvijayrajan]

post oa please there should not be much confusion in this

[shingivyas]

As a Quadrilateral a figure can either Qualify for-

 

1. Parallelogram

• the rectangle
  
• the rhombus
  
• the square

2. Trapezoid

3. Kite

 

Parallelogram...Opposite sides are parallel and equal in length,

 

We jus know.. PS II QR AND PS=QR

 

We dont know about the other opposite sides...

 

But then If the quadrilateral is anything other than parallelogram.. the parallel sides are not equal....be ita trapezoid/ kite.. ( its always the non parallels which are equal) therefore Only A would suffice.

 

So now we need to see for option D-

 

but option (ii) doesn't provide any information.. except that it qualifies for trapezoid.

Pls OA?

 

[Seeker-beliver]

After reading the entire thread ...seems like an A to me

[ayush]

Yeah answer should be A cause in the second statement even if PQ=RS doesnt conclude that PQ II RS.