Which postulate guarantees that, when two parallel lines are cut by a transversal, the corresponding angles are congruent?

Which postulate guarantees that, when two parallel lines are cut by a transversal, the corresponding angles are congruent?

• A. Corresponding Angles Postulate
• B. Alternate Interior Angles Theorem
• C. Vertical Angles Theorem
• D. Same-Side Interior Angles Theorem

Answer: (A)

When two parallel lines are cut by a transversal, angles that occupy the same position at each intersection stay equal. This exact relationship is captured by the Corresponding Angles Postulate. It says that if a transversal intersects two parallel lines, each pair of corresponding angles is congruent. So, the angle in a given corner at the first intersection has the same measure as the angle in the same corner at the second intersection. This postulate is the precise guarantee for corresponding angles. The alternate interior angles theorem refers to a different set of angles (inside the lines on opposite sides of the transversal) being equal. The vertical angles theorem concerns angles formed by two lines crossing, not the parallel-line setup. The same-side interior angles theorem deals with angles on the same side of the transversal that sum to 180 degrees, not equal measures.

When two parallel lines are cut by a transversal, angles that occupy the same position at each intersection stay equal. This exact relationship is captured by the Corresponding Angles Postulate. It says that if a transversal intersects two parallel lines, each pair of corresponding angles is congruent. So, the angle in a given corner at the first intersection has the same measure as the angle in the same corner at the second intersection.

This postulate is the precise guarantee for corresponding angles. The alternate interior angles theorem refers to a different set of angles (inside the lines on opposite sides of the transversal) being equal. The vertical angles theorem concerns angles formed by two lines crossing, not the parallel-line setup. The same-side interior angles theorem deals with angles on the same side of the transversal that sum to 180 degrees, not equal measures.