If AB is perpendicular to CD and PQ is perpendicular to AB, which of the following is/are true?

CD is parallel to PQ

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CD is perpendicular to PQ

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Both A & B

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None of the above are true

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Solution

The correct option is A
CD is parallel to PQ

If we draw everything according to the given question, we get:

In the above figure
Line PQ is perpendicular to AB.
$∴$ $∠ A P Q = ∠ Q P B = 90^{\circ}$
Line AB is perpendicular to CD.
$∴$ $∠ A B C = ∠ A B D = 90^{\circ}$
Since, the $∠ P Q B = ∠ A B D = 90^{\circ}$
$∴$ PQ is parallel to CD or vice-versa.

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