Question

Suppose you can show that Z3 and Z6 are congruent angles. Is this enough to establish that the two lines are parallel? Why or why not?

a) Yes. If corresponding angles are congruent, then the lines must be parallel.
b) No. A linear pair will always be supplementary.
c) Yes. If alternate interior angles are congruent, then the lines must be parallel.
d) No. Vertical angles will always be congruent.

Answer 1

No, showing that Z3 and Z6 are congruent angles is not enough to establish that the two lines are parallel.

Step-by-step explanation:

No, showing that Z3 and Z6 are congruent angles is not enough to establish that the two lines are parallel. To determine if two lines are parallel, you need to examine their corresponding angles or alternate interior angles. If the corresponding angles are congruent or alternate interior angles are congruent, then the lines are parallel. Therefore, the correct option is c) Yes. If alternate interior angles are congruent, then the lines must be parallel.