Question

How do I get the answers to thisQuestion 1 - 4

Answer 1

Lines d and e are parallel and lines s and t are also parallel

1. Alternate Exterior Angles Theorem

2. Corresponding Angles Postulate

3. Alternate Angles Postulate

4. Co-interior Angles Theorem

Step-by-step explanation:

Given the below;

1. Given that;

`\angle1\cong\angle4`

The theorem that justifies the above is the Alternate Exterior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

2. Given that;

`\angle2\cong\angle3`

The theorem that justifies the above is the Corresponding Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the corresponding angles are congruent.

3. Given that;

`\angle6\cong\angle7`

The theorem that justifies the above is the Alternate Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate angles are congruent.

4. Given that;

`m\angle5+m\angle8=180`

The theorem that justifies the above is the Co-interior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, angles that are in the same similar position are supplementary, that is, they add up to 180 degrees.