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Byju's Answer
Standard IX
Mathematics
The Mid-Point Theorem
In ABC,E an...
Question
In
A
B
C
,
E
and
F
are mid points of sides
A
B
and
A
C
respectively then prove that
E
F
=
1
2
B
C
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Solution
REF.Image
Given ABC is a triangle. E and F are the
mid point of side AB and AC respectively
E
D
=
B
C
E
F
+
F
D
=
B
C
F
E
+
F
E
=
B
C
2
F
E
=
B
C
E
F
=
1
2
B
C
Hence proved.
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Similar questions
Q.
In a
△
A
B
C
,
E
and
F
are the mid-point
A
B
and
A
C
respectively. Point
M
and
N
on sides
A
B
and
A
C
respectively such that
A
M
=
1
4
A
B
and
A
N
=
1
4
A
C
. Prove that
M
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=
1
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Q.
In
Δ
A
B
C
, D, E and F are mid-points of sides AB, BC and AC respectively.
Q.
Question 12
E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD, Prove that
E
F
|
|
A
B
a
n
d
E
F
=
1
2
(
A
B
+
C
D
)
.
Q.
E
and
F
are respectively the mid points of non-parallel sides
A
D
,
B
C
of a trapezium
A
B
C
D
Prove that
E
F
∥
A
B
.
Q.
In triangle
A
B
C
, angle
B
is obtuse.
D
and
E
are mid-points of sides
A
B
and
B
C
respectively and
F
is a point on side
A
C
such that
E
F
is parallel to
A
B
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B
E
F
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is a parallelogram. State True or False.
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