Given that m and n are parallel, and p is a transversal that is perpendicular to m, give an explanation for why it must also be perpendicular to n.

p is perpendicular to n. Proved.

Step-by-step explanation:

See the diagram attached.

Let us assume that mm' and nn' are two straight lines parallel to each other and pp' is a transversal.  

It is given that pp' is perpendicular to mm' i.e. ∠po'm = 90°

Now, since mm'║nn' and pp' is a transversal, so, ∠pon = ∠po'm = 90° {Those are corresponding angles}

So, pp' is also perpendicular to nn'. {Proved}