### Video Transcript

True or False: A straight line
that is perpendicular to one of two parallel lines is also perpendicular to the
other.

The best way to understand
fully what is asked here is to start by drawing a diagram. Letβs start with the straight
line. We also know that there are two
parallel lines. And one of the two parallel
lines is perpendicular to the straight line. It might also be useful if we
label the lines so that we can start to use these as part of a proof. So, letβs say that the two
parallel lines are the lines π΄π΅ and πΆπ· and the line which is perpendicular
to line π΄π΅ is the line πΈπΉ. We can also label the point
where line π΄π΅ and πΈπΉ intersect as π and where line πΆπ· and πΈπΉ intersect
as point π. If we wanted to use some
mathematical notation, we could write our facts like this.

We now need to work out if this
statement in the question is true. Is the other line, which weβve
called line πΆπ·, also perpendicular to line πΈπΉ? Since we know that we have this
relationship where the two lines are perpendicular, we can write that the
measure of angle πΈππ΅ is 90 degrees. Then, we can use the properties
of parallel lines to help us with another fact. Angles πΈππ΅ and πΈππ· are
corresponding angles, and we know that corresponding angles are equal. Since both of these angles are
equal, they are both equal to 90 degrees. Therefore, line πΈπΉ is also
perpendicular to line πΆπ·. The statement in the question
is true.

And so, we have used our
knowledge of geometry to prove a geometrical fact. By using the properties of
parallel lines, we have proved that a straight line that is perpendicular to one
of two parallel lines is also perpendicular to the other.