If two parallel lines are cut by a transversal then the bisectors of a pair of corresponding angles are?

also parallel

ask your teacher that's what the're there for

If two parallel lines are cut by a transversal (a line that intersects both parallel lines), then the bisectors of a pair of corresponding angles are also parallel. This is known as the Corresponding Angles Postulate.

To understand this concept, here's how you can prove that the bisectors of corresponding angles are parallel:

1. Start with two parallel lines, let's call them line l₁ and line l₂.
2. Draw a transversal line that intersects both l₁ and l₂. Label this line t.
3. Identify a pair of corresponding angles formed by the transversal and the two parallel lines. Let's call them angle A on line l₁ and angle B on line l₂.
4. Construct the bisectors of angle A and angle B. These bisectors divide the angles into two equal parts.
5. Now, suppose the bisectors intersect at point C.
6. By the definition of angle bisectors, angle ACP is equal to angle PCQ, and angle BCQ is equal to angle QCP, where P and Q are points on lines l₁ and l₂ respectively.
7. Since angle ACP and angle BCQ are equal (due to the definition of angle bisectors), and angle PCQ and angle QCP are equal (by the Reflexive Property of Equality), we can conclude that angle ACP is congruent to angle BCQ.
8. Using the Corresponing Angles Postulate, if angle A and angle B are congruent, and their corresponding sides are parallel (lines l₁ and l₂), then the bisectors of corresponding angles (angle ACP and angle BCQ) are also parallel.

Therefore, if two parallel lines are cut by a transversal, the bisectors of a pair of corresponding angles are parallel as well.