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Byju's Answer
Standard XII
Mathematics
Condition for Two Lines to Be Parallel
If D and ...
Question
If
D
and
E
are points on side
A
B
and
A
C
respectively of triangle
A
B
C
such that
a
r
(
Δ
D
B
C
)
=
a
r
(
Δ
E
B
C
)
, then prove that
D
E
∥
B
C
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Solution
If Area
(
△
D
B
C
)
=
Area
(
△
E
B
C
)
then
1
2
|
B
C
|
|
D
F
|
=
1
2
|
B
C
|
|
E
G
|
|
D
F
|
=
|
E
G
|
Also
E
G
⊥
B
C
&
D
F
⊥
B
C
then
D
&
E
are equidistant from
B
C
and
D
E
∥
B
C
because line joining equidistant point from a line is
∥
to that line
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Similar questions
Q.
If
D
and
E
are points on sides
A
B
and
A
C
respectively of a
△
ABC such that DE
∥
BC and
B
D
=
C
E
.
Prove that
△
ABC is isosceles.
Q.
If
d
and
e
are points on sides
A
B
and
A
C
respectively of a
△
a
b
c
such that
D
E
∥
B
C
and
B
D
=
C
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. Prove triangle
a
b
c
is isosceles.
Q.
D
and
E
are points on sides
A
B
and
A
C
respectively of
△
A
B
C
such that
a
r
e
a
(
D
B
C
)
=
a
r
e
a
(
E
B
C
)
. Prove that
D
E
∥
B
C
Q.
D and E are points on sides AB and AC respectively of triangle ABC such that ar(DBC)
=
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Q.
In
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Standard XII Mathematics
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