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Byju's Answer
Standard IX
Mathematics
Trapezium
PQRS is a tra...
Question
P
Q
R
S
is a trapezium in which
P
Q
∥
R
S
and its diagonal intersect each at the point
O
.
Prove that
P
O
Q
O
=
R
O
S
O
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Solution
As
P
Q
|
|
R
S
and
P
R
and
Q
S
are transversal
∠
O
S
R
=
∠
O
Q
P
(alternate angles)
∠
O
R
S
=
∠
O
P
Q
(alternate angles)
∴
△
S
O
R
∼
△
P
O
Q
⇒
S
O
P
O
=
R
O
Q
O
=
S
R
P
Q
⇒
S
O
P
O
=
R
O
Q
O
⇒
Q
O
P
O
=
R
O
S
O
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