anant07 wrote:
Is quadrilateral ABCD a parallelogram?
(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC
In order to prove that a quadrilateral is a parallelogram at least one of the following should be true:--
1. Two pairs of opposite sides are equal or parallel
2. One pair of opposite side is equal and parallel
3. Both the pairs of opposites angles are equal
4. Diagonals bisect each other
Considering the problem
STAT1 : Area of Triangle ABC = Area of Triangle ACD
From this we just know that there is a diagonal AC and on it's two sides there are two triangles which have same area. IF we would have given that the base of these two triangles are equal and parallel then we could prove that the quadrilateral is a parallelogram. But not we can't.
STAT2: It just tells us that two adjacent are equal. Which is of no use to us.
Combining these two also doesn't give us any concrete information to prove that the figure is a parallelogram.
So, INSUFFICIENT
Hence, Answer will be E
Hope it helps!
hi , from st(2) , if adjacent sides are equal , can't we say its not a parallelogram , as in a parallelogram oppo. sides are equal