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Byju's Answer
Standard IX
Mathematics
The Mid-Point Theorem
In the quadri...
Question
In the quadrilateral (1) given below,
A
B
|
|
D
C
,
E
and
F
are mid point of
A
D
and
B
D
respectively. Prove that
E
G
=
1
2
(
A
B
+
D
C
)
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Solution
Given:-
A
B
∥
D
C
,
E
and
F
are mid-points of
A
D
and
B
D
respectively.
To prove:-
E
G
=
1
2
(
A
B
+
D
C
)
Proof:-
In
△
A
B
D
,
D
F
=
B
F
(
∵
F is the mid-point of BD
)
Also,
E
is the mid-point of
A
D
(
Given
)
Therefore,
E
F
∥
A
B
and
E
F
=
1
2
A
B
.
.
.
.
.
(
1
)
⇒
E
G
∥
C
D
(
∵
A
B
∥
C
D
)
Now,
F
is the mid-point of
B
D
and
F
G
∥
D
C
∴
G
is the mid-point of
B
C
⇒
F
G
=
1
2
C
D
.
.
.
.
.
(
2
)
Adding equation
(
1
)
&
(
2
)
, we have
E
F
+
F
G
=
1
2
A
B
+
1
2
D
C
⇒
E
G
=
1
2
(
A
B
+
C
D
)
Hence proved.
Suggest Corrections
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Similar questions
Q.
In the quadrilateral (1) given below,
A
B
|
|
D
C
,
E
and
F
are mid point of
A
D
and
B
D
respectively. Prove that
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Q.
In the quadrilateral given below,
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+
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M
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Q.
A
B
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D
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and
F
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C
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A
B
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1
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Q.
In the quadrilateral given below,
A
D
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.
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