Question

ABCD is a square and EF is parallel to diagonal DB and EM=FM .Prove that BF=DE and AM bisects angle BAD

Answer 1

given that,

ABCD is a square
EF parallel to DB
and EM = FM

to prove,
BF = DE
and AM bisects angle BAD.

construction,
let the the point on AM be O

proof ,
in triangle ADO and BAO
AD = AB ( all sides are equal in square )
DO = OB (M is cutting the diagonal DM in 2 equal parts )
AO = AO ( common )

therefore but sss congurance rule ,
triangle ADO is congurant to triangle BAO.

so, AM bisects angle BAD ( by c.p.c.t )


DC = BC ( all side are equal in square E and F is the mid point of DC and BC )
therefore ,
BF = DE .

hence proved.