Question

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

• A. CD is parallel to PQ
• B. CD is perpendicular to PQ
• C. Both A & B
• D. None of the above are true

Answer 1

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.
$\therefore$$\angle APQ=\angle QPB={90}^{\circ }$
Line AB is perpendicular to CD.
$\therefore$$\angle ABC=\angle ABD={90}^{\circ }$
Since, the $\angle PQB=\angle ABD={90}^{\circ }$
$\therefore$ PQ is parallel to CD or vice-versa.