Video Transcript
True or False: In the given figure,
the two straight lines 𝐴𝐵 and 𝐶𝐷 are parallel.
We can begin this question by
identifying the two lines 𝐴𝐵 and 𝐶𝐷 on the figure. And we aren’t given any line
markings to indicate that these lines are parallel. But instead we are given the
measures of two angles as 75 degrees each.
We can consider the angle 𝐷𝑁𝐹
first. We recall that when two straight
lines intersect, the vertically opposite angles are equal in measure. And because lines 𝐷𝐶 and 𝐸𝐹
intersect, then we can say that angle 𝐸𝑁𝐶 is vertically opposite angle
𝐷𝑁𝐹. So these angles are equal in
measure. They are both 75 degrees.
We can now observe that there is
another pair of congruent angle measures, because the measure of angles 𝐸𝑁𝐶 and
𝐸𝑀𝐴 are both 75 degrees. We could describe these two angles
as corresponding angles. And this leads us to another
important property. It is that if the corresponding
angles that a transversal makes with a pair of lines are congruent, then the pair of
lines is parallel. We have got corresponding angles
congruent. Therefore, the pair of lines is
parallel. And so the statement in the
question is true, because the lines 𝐴𝐵 and 𝐶𝐷 are parallel.
Notice that it would also have been
equally valid to prove this statement is true by first demonstrating that angles
𝐵𝑀𝐹 and 𝐸𝑀𝐴 are vertically opposite angles and therefore congruent. And then we could have applied the
same second property to identify that angles 𝐵𝑀𝐹 and 𝐷𝑁𝐹 are corresponding
congruent angles to prove that the lines 𝐴𝐵 and 𝐶𝐷 are parallel. Either method would prove the
statement is true.
