To prove that the bisectors of any pair of corresponding angles formed by a transversal intersecting two parallel lines are parallel, we can follow these steps:

1. Let's consider two parallel lines 'a' and 'b' intersected by a transversal 't'. This will form corresponding angles ∠1 and ∠2.

2. Let's bisect these angles to form ∠1a and ∠1b from ∠1, and ∠2a and ∠2b from ∠2.

3. By the definition of angle bisectors, ∠1a = ∠1b and ∠2a = ∠2b.

4. Since ∠1 and ∠2 are corresponding angles formed by a transversal intersecting two parallel lines, by the Corresponding Angles Postulate, ∠1 = ∠2.

5. Therefore, if ∠1 = ∠2, and ∠1a = ∠1b and ∠2a = ∠2b, then ∠1a = ∠2a and ∠1b = ∠2b.

6. If ∠1a = ∠2a and ∠1b = ∠2b, then the lines forming these angles are parallel, by the Converse of the Corresponding Angles Postulate.

7. Therefore, the bisectors of any pair of corresponding angles formed by a transversal intersecting two parallel lines are parallel.

This completes the proof.

Question

To prove that the bisectors of any pair of corresponding angles formed by a transversal intersecting two parallel lines are parallel, we can follow these steps:

1. Let's consider two parallel lines 'a' and 'b' intersected by a transversal 't'. This will form corresponding angles ∠1 and ∠2.

2. Let's bisect these angles to form ∠1a and ∠1b from ∠1, and ∠2a and ∠2b from ∠2.

3. By the definition of angle bisectors, ∠1a = ∠1b and ∠2a = ∠2b.

4. Since ∠1 and ∠2 are corresponding angles formed by a transversal intersecting two parallel lines, by the Corresponding Angles Postulate, ∠1 = ∠2.

5. Therefore, if ∠1 = ∠2, and ∠1a = ∠1b and ∠2a = ∠2b, then ∠1a = ∠2a and ∠1b = ∠2b.

6. If ∠1a = ∠2a and ∠1b = ∠2b, then the lines forming these angles are parallel, by the Converse of the Corresponding Angles Postulate.

7. Therefore, the bisectors of any pair of corresponding angles formed by a transversal intersecting two parallel lines are parallel.

This completes the proof.

Knowee AI · Accepted Answer