Consider the diagram.

Question

Parallel lines r and s are cut by transversal q. On line r where it intersects line q, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line s where it intersects line q, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5.

Given that r||s and q is a transversal, we know that by the [________].

corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Answer 1

Given that lines \( r \) and \( s \) are parallel and line \( q \) is a transversal, we can apply the corresponding angles theorem.

According to this theorem, if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. For example, angle 1 on line \( r \) corresponds to angle 5 on line \( s \), and angle 2 corresponds to angle 6.

So the complete statement would be: "Given that \( r \parallel s \) and \( q \) is a transversal, we know that by the corresponding angles theorem."