Is quadrilateral ABCD a rectangle?

Question

(1) Angle ABC = 90 degrees
(2) AB = CD

Bunuel · Accepted Answer

A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle. (1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient. (2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient. (1)+(2) Look at the diagram: rectangle.PNG It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient. It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa). Hope it helps.

adishail · Answer

E

1. ABC = 90 ................ other angles can be of any value.

2. AB = CD ............... AC and BD might not be equal.

For rectangle, all angles have to be equal (hence, 90) and opposite sides should be equal. Neither of the two statement helps in determining if the two requirements are satisfied or not.

saxenashobhit · Answer

E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

agnok · Answer

The diagram made the difference in understanding the answer.. thanks

saxenashobhit · Answer

Thanks Bunuel for the diagram

PathFinder007 · Answer

HI Bunnel,

One doubt. Here it is mentioned that angle ABC are 90 degrees. and quadrilateral have total of 360 degree. so fourth one should be 90 degree.

then why you have mentioned following statement.

angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient

Thanks

Bunuel · Answer

Yes, the Sum of Interior Angles of a polygon is  180(n-2)  degrees, where  n  is the number of sides (so is the number of angles). Thus the sum of the interior angles of a quadrilateral is 180*2=360 degrees.

But knowing that one of the angles of a quadrilateral is 90 degrees does not mean that the other angles must also be 90 degrees. The sum of the remaining three angles must be 360-90=270 degrees. So, the remaining three angles can be 100, 100 and 70 or 100, 110, and 60, ...

Hope it's clear.

ravishankar1788 · Answer

Q1. 
statement1>parallelogram 
statement2>rectangle only if statement1 is true 
answer:"C" 
Q2. 
answer:"B" 
Q3 
statement1>rectangle meaning all angles are 90 
statement2> rhombus... 
together it becomes a square..answer:"C"

Bunuel · Answer

Please note that the OA is E, not C. Check here: is-quadrilateral-abcd-a-rectangle-100729.html#p778263 Hope it helps.

bumpbot · Answer

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Is quadrilateral ABCD a rectangle?

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Is quadrilateral ABCD a rectangle?

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