86.9k views
5 votes
Two of these lines are parallel. If it is uncertain whether or not the lines are parallel, can the comparison be made? Explain.

Two of these lines are parallel. If it is uncertain whether or not the lines are parallel-example-1
User Tornike
by
3.2k points

1 Answer

4 votes

Remember that when parallel lines are cut by a transversal, there are pairs of angles formed. Some of those pairs are congruent while the others are supplementary.

In the given diagram, the angles x and a are corresponding angles, so they are congruent. Then:


m\angle x=m\angle a

This only happens when there is a pair of parallel lines. Otherwise, we would have to know the measure of the angle a in order to compare it to the angle x.

Then, the comparison cannot be made if it is uncertain whether or not the lines are parallel.

User Muhannad Fakhouri
by
3.4k points