Question

In the following figure, AB and CD both are perpendicular to the same line PQ.
Identify the lines AB, CD, PQ. Show by giving suitable reasons, that AB is || CD.

Answer 1

AB and CD both are perpendicular to the same line PQ.
Then,
$\angle ABQ={90}^o$ and also $\angle CDQ={90}^o$
$\angle ABQ=\angle CDQ$
Since, they are corresponding angles then AB $\parallel$ CD. [If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.]