Question

1. a transversal cuts two parallel lines so that corresponding angles are supplementary. what must be true about the transversal?

Explanation:

Step1: Recall properties of parallel lines and transversals

When two parallel lines are cut by a transversal, corresponding angles are congruent (equal in measure). Let the measure of each pair of corresponding angles be \(x\) and \(x\).

Step2: Use the supplementary - angle condition

We are given that corresponding angles are supplementary. So \(x + x=180^{\circ}\). Solving for \(x\), we have \(2x = 180^{\circ}\), then \(x = 90^{\circ}\).

Step3: Determine the nature of the transversal

If the corresponding angles formed by a transversal and two parallel lines are \(90^{\circ}\), then the transversal is perpendicular to the parallel lines.

Answer:

The transversal is perpendicular to the two parallel lines.