Question

ABCD is a parallelogram and Mis the mid-point of the diagonal BD. A segment is drawn through M, which meets AD at E and BC at F. Prove that M bisects EF.​

Answer 1

Answer:

Given, E is mid point of AD

Also EB∥DF

⇒ B is mid point of AF [mid--point theorem]

so, AF=2AB (1)

Since, ABCD is a parallelogram,

CD=AB

⇒AF=2CD

AD∥BC⇒LB∥AD

In ΔFDA

⇒LB∥AD

⇒

LD

LF

=

AB

FB

=1 from (1)

⇒LF=LD

so, DF=2DL