Latest Elitmus Aptitude Question SOLUTION: In ABCD Quadrilateral, a parallogram? (i)angle ABC is 90 DEGREE (ii)angle ADC is 90 DEGREE (a) (b) (c) (d)

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(#M40094393) ELITMUS Logical Reasoning question data sufficiency Keep an EYE

In ABCD Quadrilateral, a parallogram?
(i)angle ABC is 90 DEGREE
(ii)angle ADC is 90 DEGREE


(a) (b) (c) (d)

Asked In Elitmus shaik umme rumana (9 years ago)

Unsolved Read Solution (16)

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Read Solution (16) :

Siddartha Mulumudi  (9 years ago)

Both statements are necessary..
Because for a quadrelatral to become a parllelogrm. one set of opposite angles should be equal (automatically 2nd set becomes equal if so)

Here ABC = ADC = 90 which are opposite angles.
More simplified it becomes a rectangle which is also a parllelogram

Is this solution Helpfull? Yes (19) | No (12)  

sanchit  (9 years ago)

no statement is sufficient because
A |
|
|
| D
B |____/
c
In this case Both angles are 90
but this is not a paralllelgram

Is this solution Helpfull? Yes (7) | No (9)  

shaik umme rumana  (9 years ago)

both statements are necessary

Is this solution Helpfull? Yes (5) | No (5)  

RITUPARNA DHAR  (9 years ago)

none of the given statements are necessary...the quadrilateral has two opposite equal angles..that does not imply that it is a parallelogram...

Is this solution Helpfull? Yes (4) | No (1)  

binesh kumar  (9 years ago)

for Quadrilateral angle ABC + angle ADC =180
(1)+(2) = 180
therefore both equation help for quadrilateral
option C

Is this solution Helpfull? Yes (3) | No (5)  

Siddartha Mulumudi  (7 years ago)

Kindly note that, every sqauare and rectangle is one of the type of parallogram. More simplified

Square (subset of) Rectangle (subset of) parallelogram (subset of) Quardrilateral. Most of them has mentioned in the solutions in the below manner

1. If one pair of opposite angles are equal it's not a parallelogram.
(No. This solution is wrong). If one pair of opposite angles of a quadrilateral are equal, then automatically the other pair of opposite angles will be equal.

2. If the angle is 90deg then it is either a rectangle or square and not a parallelogram
(By the defination of rectangle: A parallelogram whose opposite angles are 90deg is a rectangle and if the length of the adjacent sides are also equal then it's a square.

So, from the question to prove that ABCD is a parallelogram both statements are necessary. And in this scenario the quadrilateral would either be a square or a rectangle which are one of the types of PARALLELOGRAM

Is this solution Helpfull? Yes (2) | No   

Mogal Fayaz Baig  (9 years ago)

Both are insufficient .
If both angles are 90 then it will be a square or a rectangle

Is this solution Helpfull? Yes (1) | No (11)  

Suvrajit Chatterjee  (8 years ago)

For parallelogram opposite angles should be equal , that is ok. but it should not be equal to 90 degree. Two opposite pairs are greater than 90 and other two opposite pairs are less than 90 degree. So answer should be none of above statements are sufficient

Is this solution Helpfull? Yes (1) | No   

SOWMYA CHITHALOORI  (8 years ago)

either of statement is enough to say one angle is 90 all other are obv. 90 as the sum of adj. angle in a ||grm is 180 ; and all rectangles are parallelograms

Is this solution Helpfull? Yes (1) | No (1)  

Vivek Kumar Wadhawan  (8 years ago)

for a parallelogram if angle ABC is 90 Degree than it is compulsory that angle ADC to be 90 Degree.
but if ABC is not 90 Degree then ADC will also not 90 Degree, In other words for an Parallelogram angle ABC should equal to angle ADC.

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raaz yadav  (9 years ago)

both conditions should b there ..
for any quadiletral to become a parallelogram atleast any two opposite angle should be equal ...
if angle ABC = Angle ADC =90 then it become a rectangle or square that is also a parallogram ..

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Ehtesham  (9 years ago)

necessary condition for parallelogram:
1).both pair of opposite angles should be congruent .ie if ABCD is parallelogram then,

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bhagya shri  (9 years ago)

ans- any single statement is necessary ... to find out that it is parallogram or not ... becouse parallogram does not have 90 angle

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Mahendra Jakhar  (8 years ago)

A it is!!
_| so |-

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DEEPAK RAJ  (8 years ago)

Those who are saying that it is a rectangle not a parllelogram. Rectangle is also a parllelogram in which both opposite angles are 90 degree. Similarly rhombus and square are also a parallelogram.

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Ashutosh Aman  (8 years ago)

Including Both statement says that one pair of opposite set of angle in quadrilateral is equal and 90. But there is no way in which you can prove that quadrilateral is parallelogram.

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