Question

In a parallelogram ABCD, E and F are the midpoints of AB and CD respectively. Show that BD bisects EF.
MATHS STD 8

Answer 1

Answer:-

In ABD;

AO||AD [ABCD is a parallelogram and the line drawn on the mids are parallel]

E is the mid of AB [Given]

thus, O is the mid of DB [Converse mid point theorem]

In BDC;

FO||BC [ANCD is a parallelogram and the line drawn on the mids are parallel]

F is the mid of DC [Given]

thus, O is the mid of DB [ Converse mid point theorem]

In both the above cases O is the mid of DB as well as EF

• Hence ,it's proved that DB bisects EF.