Question

Prove with statement and reasons that two lines perpendicular to the same line are parallel to each other.

Answer 1

Assume both lines are different .(one does not lie on other)
see if they are not parallel they would meet at some point P say .

but then <P=0 (angles in a triangle sum to 180) .this is possible only if one line lies on the other .
therefore we have a contradiction

Now Assume both lines lie on one other ,and perpendicular to some line , without the hypothesis ,both lines are parallel.

So in both cases we have proved