Is quadrilateral ABCD a rectangle?A rectangle is a quadrilateral with four right angles
1. angle ABC = 90 degrees
Please explain your solution.
- 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:
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.
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
It may be a square.
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.
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