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Standard VI
Mathematics
Question
In the given figure,
A
B
and
C
D
are intersecting at
′
O
′
,
O
A
=
O
B
and
O
D
=
O
C
. Show that
A
D
∥
B
C
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Solution
Verified by Toppr
From the figure,
O
A
=
O
B
and
O
D
=
O
C
Line
C
D
and
A
B
intersect
∴
∠
A
O
D
=
∠
B
O
C
[Vertically opposite angles]
In
△
A
O
D
and
△
B
O
C
,
O
A
=
O
B
∠
A
O
D
=
∠
B
O
C
∴
△
A
O
D
≅
△
B
O
C
[SAS Congruence Rule]
O
D
=
O
D
⇒
∠
O
A
D
=
∠
O
B
C
[by CPCT]
But
∠
O
A
D
and
∠
O
B
C
form a pair of alternate angles.
If a transversal intersects two lines such that pair of alternate interior angles is equal, then lines are parallel.
⇒
A
D
|
|
B
C
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Similar Questions
Q1
In the given figure,
A
B
and
C
D
are intersecting at
′
O
′
,
O
A
=
O
B
and
O
D
=
O
C
. Show that
A
D
∥
B
C
View Solution
Q2
In the given figure,
A
B
and
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D
intersect at
′
O
′
,
O
A
=
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B
and
O
D
=
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C
. Show that
△
A
O
D
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.
View Solution
Q3
The given figure shows a trapezium
A
B
C
D
in which
A
B
is parallel to
D
C
and
A
D
=
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C
.
Prove that :
O
A
=
O
B
and
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=
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View Solution
Q4
In the figure OA = OB and OD = OC Show that
(a)
△
A
O
D
≅
△
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O
C
(b) AD || BC
View Solution
Q5
In the trapezium ABCD, AD || BC and the diagonals intersect at O. Prove that
.