Given that p is perpendicular to q and q is parallel to r. Prove that p is perpendicular to r

Answer 1

Because the right angles transfer from p to q since p || q.

Here's a formal proof:

M and N are the intersection points of P and Q and P and R respectively.

P is on p, R is on r, and Q is on q respectively

Angle PMQ is a right angle since p is perpendicular to Q.

Angles PMQ and PNR are alternate angles, which are congruent since

p || q

Then PNR is a right angle since alternate angles formed by parallel lines

are congruent.

THerefore, p is perpendicular to r.