Question

1. choose the conclusion that could be made using the given postulate and given lines a and b are parallel:

alternate interior angles are congruent
a ∠3 = ∠7
b ∠7 = ∠6
c ∠1 = ∠8
d ∠3 = ∠6

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal.

Step2: Analyze each option

• Option A: \(\angle3\) and \(\angle7\) are not alternate interior angles.
• Option B: \(\angle7\) and \(\angle6\) are adjacent angles (linear pair), not alternate interior angles.
• Option C: \(\angle1\) and \(\angle8\) are not alternate interior angles.
• Option D: \(\angle3\) and \(\angle6\) are non - adjacent interior angles that lie on opposite sides of the transversal. So, by the Alternate Interior Angles Theorem (if two parallel lines are cut by a transversal, then alternate interior angles are congruent), when \(a\parallel b\), \(\angle3=\angle6\)

Answer:

D. \(\angle3 = \angle6\)