Is quadrilateral ABCD a rectangle?

Question

ABCD.PNG Is quadrilateral ABCD a rectangle? (1) The area of triangle ABD is one-half the area of ABCD (2) The area of triangle ABC is one-half the area of ABCD

GMATinsight · Answer

Question: Is quadrilateral ABCD a rectangle?

STatement 1 : The area of triangle ABD is one-half the area of ABCD

i.e. ABCD is a parallelogram which may or may NOT be a rectangle hence

NOT SUFFICIENT

Statement 2 : The area of triangle ABC is one-half the area of ABCD

i.e. ABCD is a parallelogram which may or may NOT be a rectangle hence

NOT SUFFICIENT

Combining the statements

i.e. ABCD is a parallelogram which may or may NOT be a rectangle hence

NOT SUFFICIENT

Answer: Option E

preetamsaha · Answer

STatement 1: The area of triangle ABD is one-half the area of ABCD
i.e. ABCD may be a rectangle or may be a square NOT SUFFICIENT

Statement 2: The area of triangle ABC is one-half the area of ABCD
i.e. ABCD may be a rectangle or may be a square NOT SUFFICIENT

Combining 1 and 2
ABCD may be a rectangle or may be a square NOT SUFFICIENT

correct answer E

GMATBusters · Answer

(1) The area of triangle ABD is one-half the area of ABCD
This is true for any parallelogram, hence we cannot be sure that ABCD is a Rectangle.

(2) The area of triangle ABC is one-half the area of ABCD
This is true for any parallelogram, hence we cannot be sure that ABCD is a Rectangle.

Even after combing both, we cannot be sure that ABCD is a Rectangle.
Answer E.

To prove a  parallelogram  to be Rectangle:
1) all angles are equal
2) both diagonals are equal

Remember: Any Quadrilateral with equal diagonals need not be Rectangle. The Equal diagonals must bisect each other for the quadrilateral to be qualified as a Rectangle.

https://gmatclub.com/forum/download/file.php?id=53649

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Is quadrilateral ABCD a rectangle?

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