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. Let’s 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, let’s say that the two
parallel lines are the lines 𝐴𝐵 and 𝐶𝐷 and the line which is perpendicular
to line 𝐴𝐵 is the line 𝐸𝐹. We can also label the point
where line 𝐴𝐵 and 𝐸𝐹 intersect as 𝑃 and where line 𝐶𝐷 and 𝐸𝐹 intersect
as point 𝑄. 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 we’ve
called line 𝐶𝐷, also perpendicular to line 𝐸𝐹? Since we know that we have this
relationship where the two lines are perpendicular, we can write that the
measure of angle 𝐸𝑃𝐵 is 90 degrees. Then, we can use the properties
of parallel lines to help us with another fact. Angles 𝐸𝑃𝐵 and 𝐸𝑄𝐷 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 𝐸𝐹 is also
perpendicular to line 𝐶𝐷. 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.
