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Byju's Answer
Standard X
Mathematics
AAA Similarity
D,E and F a...
Question
D
,
E
and
F
are respectively the mid-point of the sides
B
C
,
C
A
and
A
B
of a
△
A
B
C
Show that
a
r
(
B
D
E
F
)
=
1
2
a
r
(
A
B
C
)
Open in App
Solution
As we have ar
(
D
E
F
)
=
1
4
a
r
(
A
B
C
)
2
×
a
r
(
D
E
F
)
=
2
4
a
r
(
A
B
C
)
2
a
r
(
D
E
F
)
=
1
2
a
r
(
A
B
C
)
a
r
(
D
E
F
)
+
a
r
(
D
E
F
)
=
1
2
a
r
(
A
B
C
)
a
r
(
D
E
F
)
+
a
r
(
F
B
D
)
=
1
2
a
r
(
A
B
C
)
a
r
(
B
D
E
F
)
=
1
2
a
r
(
A
B
C
)
∴
Proved .
Suggest Corrections
0
Similar questions
Q.
In the figure
△
A
B
C
,
D
,
E
,
F
are the midpoint of sides
B
C
,
C
A
and
A
B
respectively. Show that
a
r
(
B
D
E
F
)
=
1
2
a
r
(
△
A
B
C
)
Q.
D
,
E
and
F
are respectively the mid-points of the sides
B
C
,
C
A
and
A
B
of a
△
A
B
C
.
Show that
(i)
B
D
E
F
is a parallelogram
(ii)
a
r
(
D
E
F
)
=
1
4
a
r
(
A
B
C
)
(iii)
a
r
(
B
D
E
F
)
=
1
2
a
r
(
A
B
C
)
Q.
D
,
E
and
F
are respectively the mid-points of the sides
B
C
,
C
A
and
A
B
of a
Δ
A
B
C
.
Show that
(a)
B
D
E
F
is a parallelogram.
(b)
ar
(
D
E
F
)
=
1
4
ar
(
A
B
C
)
(c)
ar
(
B
D
E
F
)
=
1
2
ar
(
A
B
C
)
Q.
D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. Show that
Q.
State the whether given statement is true or false
ΔABC, D, E and F are midpoints of sides AB, BC and CA respectively.Prove
a
r
(
B
D
E
F
)
=
1
2
a
r
(
△
A
B
C
)
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