Answers:
4. Alternate Exterior Angles Theorem
5. Corresponding Angles Postulate
6. Same-Side Interior Angles Theorem
7. Linear Pair Postulate
8. Vertical Angles Theorem
Given the figure of 2 parallel lines cut by a transversal, we are to state the postulate or theorem that justifies each conclusion.
4. ∠1 ≅ ∠8
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. This theorem is called Alternate Exterior Angles Theorem.
5. ∠3 ≅ ∠7
If two parallel lines are cut by a transversal, then its corresponding angles are congruent. This is called the Corresponding Angles Postulate.
6. ∠4 is supplementary to ∠6
If two parallel lines are cut by a transversal, then, interior angles on the same side of the transversal are supplementary. This is the Same-Side Interior Angles Theorem.
7. ∠3 is supplementary to ∠4
This involves two theorems, the Same-Side Interior Angles Theorem, and the Alternate Interior Angles Theorem, which state that if a parallel line is cut by a transversal, then, alternate interior angles are congruent.
Another way to prove this is by Linear Pair Postulate, which states that if two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees.
8. ∠7 ≅ ∠6
If angles are opposite each other and formed by two intersecting straight lines, then its vertical angles are congruent. This is called the Vertical Angles Theorem.