Question

what postulate or theorem justifies each of the following statements. 1. ∠1≅∠5 2. ∠4 and ∠6 are supplementary. 3. ∠4≅∠5 4. ∠2≅∠7

Explanation:

Step1: Identify angle - pair type for ∠1 and ∠5

∠1 and ∠5 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. This is the Corresponding Angles Postulate.

Step2: Identify angle - pair type for ∠4 and ∠6

∠4 and ∠6 are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary. This is the Same - Side Interior Angles Theorem.

Step3: Identify angle - pair type for ∠4 and ∠5

∠4 and ∠5 are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent. This is the Alternate Interior Angles Theorem.

Step4: Identify angle - pair type for ∠2 and ∠7

∠2 and ∠7 are alternate exterior angles. When two parallel lines are cut by a transversal, alternate exterior angles are congruent. This is the Alternate Exterior Angles Theorem.

Answer:

1. Corresponding Angles Postulate
2. Same - Side Interior Angles Theorem
3. Alternate Interior Angles Theorem
4. Alternate Exterior Angles Theorem