Question

In the diagram, the lines dividing the parking spaces are parallel. What must be true about 41 and 22? What theorem

supports your conclusion?
A. 1 and 22 are supplementary, alternate interior angles theorem
B. Z1 Z2; alternate interior angles theorem
C. and 2 are supplementary, consecutive interior angles theorem
D. Z1 Z2, consecutive interior angles theorem

Answer 1

B. ∠1 ≅ ∠2; alternate interior angles theorem

Explanation:

The Alternate Interior Angles theorem states, if two parallel lines (in this problem, the lines dividing the parking spaces) are cut by a transversal, then the pairs of alternate interior angles (in this problem, ∠1 and ∠2) are congruent.

You can check this result graphically, imagine you move the transversal line, so that, ∠1 increases, then ∠2 also increases, and if ∠1 decreases, then ∠2 also decreases.