Statement 1: AC is perpendicular to BD.susha0df wrote:If ABCD is a quadrilateral, is AB=BC=CD=DA?
(1) AC is perpendicular to BD
(2) AB+CD=BC+AD
As there is no restrictions on the lengths of the sides, they can be same or different.
Not sufficient
Statement 2: AB + CD = BC + AD
There can be various possible combinations of lengths satisfying this condition.
Not sufficient
1 & 2 Together: Choose AB = AD and CD = BC, then statement 2 satisfies and we can make AC perpendicular to BD (as shown in the figure below) but still lengths of all the sides are not same.
Same case for AB = BC and CD = AD.
Not sufficient.
The correct answer is E.
