A city planner needs to verify that Main Street and Oak Street are parallel to each other. Which angles must be congruent to prove this?
To verify that Main Street and Oak Street are parallel, we need to prove that the corresponding angles are congruent. Therefore, the angles that must be congruent to prove this are:
1) Corresponding Angles: When a transversal line intersects two parallel lines, the corresponding angles formed on the same side of the transversal line are congruent. In this case, the corresponding angles on Main Street and Oak Street must be congruent.
2) Alternate Interior Angles: When a transversal line intersects two parallel lines, the alternate interior angles formed on the inside of the parallel lines are congruent. So, the alternate interior angles between Main Street and Oak Street also need to be congruent.
Therefore, the corresponding angles and the alternate interior angles must be congruent to prove that Main Street and Oak Street are parallel.