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Standard XII
Maths
Question
Given a parallelogram ABCD. Prove that
O
C
=
O
A
Open in App
Solution
Verified by Toppr
Given:-
A
B
C
D
is a parallelogram with
A
C
&
B
D
as diagonals.
A
B
C
D
is a parallelogram.
∴
A
D
∥
B
C
⟹
∠
B
D
A
=
∠
C
B
D
and
∠
D
A
C
=
∠
A
C
B
...... (alternate angles)
o
r
∠
O
D
A
=
∠
C
B
O
and
∠
D
A
O
=
∠
O
C
B
.
.
.
.
.
.
.
.
(
i
)
Now between
Δ
A
D
O
and
Δ
C
O
B
we have
A
D
=
B
C
...... (opposite side of a parallelogram)
∠
O
D
A
=
∠
C
B
O
and
∠
D
A
O
=
∠
O
C
B
..... by
(
i
)
∴
By ASA test
Δ
A
O
D
and
Δ
C
O
B
are congruent.
∴
O
C
=
O
A
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Similar Questions
Q1
Given a parallelogram ABCD. Prove that
O
C
=
O
A
View Solution
Q2
Given a parallelogram ABCD. Prove that
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Q3
If O is a point within a quadrilateral ABCD, prove that ;
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+
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>
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.
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Q4
The given figure shows a trapezium
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in which
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is parallel to
D
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and
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.
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View Solution
Q5
'
O
' is any point inside a rectangle
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.
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