Question

8.
ABCD
is
a
rhombus
,
EABF
is
a
straight
line
such
that
EA
=
AB
=
BF
.
Prove
that
ED
and
FC
when​

Answer 1

Answer:

ANSWER

We know that the diagonals of a rhombus are perpendicular bisector of each other.

∴OA=OC,OB=OD,∠AOD=∠COD=90

∘

and, ∠AOB=∠COB=90

∘

In ΔBDE, A and O are mid - points of BE and

BD respectively.

∴OA∥DE

⇒OC∥DG

In ΔCFA,B and O are mid - points AF and AC respectively

∴OB∥CF

⇒OD∥GC

Thus, in quadrilateral DOCG, we have

OC∥DG and OD∥GC

⇒DOCG is a parallelogram.

∴∠DGC=∠DOC

⇒∠DGC=