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Byju's Answer
Standard VIII
Mathematics
Parallelogram
In Fig. 17.29...
Question
In Fig. 17.29, suppose it is known that DE = DF. Then, is ΔABC isosceles? Why or why not?
Fig. 17.29
Open in App
Solution
In
∆
FDE
:
DE
=
DF
∴
∠
FED
=
∠
DFE
.
.
.
.
.
.
.
.
.
.
.
.
.
(
i
)
(
angles
opposite
to
equal
sides
)
In
the
II
gm
BDEF
:
∠
FBD
=
∠
FED
.
.
.
.
.
.
.
(
ii
)
(
opposite
angles
of
a
parallelogram
are
equal
)
In
the
II
gm
DCEF
:
∠
DCE
=
∠
DFE
.
.
.
.
.
.
(
iii
)
(
opposite
angles
of
a
parallelogram
are
equal
)
From
equations
(
i
)
,
(
ii
)
and
(
iii
)
:
∠
FBD
=
∠
DCE
In
△
ABC
:
If
∠
FBD
=
∠
DCE
,
then
AB
=
AC
(
sides
opposite
to
equal
angles
)
.
Hence
,
△
ABC
is
isosceles
.
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Similar questions
Q.
In Fig. 17.29, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not?
