question_answer

Let ABCD be a parallelogram and let E be the midpoint of side AB. If EC is perpendicular to ED, then:

A)  \[ED=EC\]       

B)         \[EB=EC\]

C)  \[EA=ED\]       

D)        \[EC+ED=2BC\]

E)  \[EC+ED=2DC\]

Correct Answer: E

Solution :

From figure, it is clear \[ED\ne EC\] Then \[EB\ne BC\]and \[EA\ne ED\] And \[ED>BC,\] \[EC>BC\] \[\Rightarrow \]               \[EC+ED>2BC\] Hence,       \[EC+ED=2DC\]