Question

line r and line s are parallel. answer the following about the given figure. (lesson 4.2)
(1 point)
c. which angle pairs are alternate interior angles? list all angle pairs.
d. what theorem explains why \\( \angle 4 \cong \angle 8 \\)?
e. which angle pairs are same - side interior angles? list all angle pairs.

Explanation:

Step1: Identify alternate interior angles

Alternate interior angles are non - adjacent angles that lie between the two parallel lines and on opposite sides of the transversal.
For lines \(r\) and \(s\) with transversal \(l\), the pairs are \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\)

Step2: Determine the theorem for \(\angle4\cong\angle8\)

\(\angle4\) and \(\angle8\) are corresponding angles. The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

Step3: Identify same - side interior angles

Same - side interior angles are non - adjacent angles that lie between the two parallel lines and on the same side of the transversal.
For lines \(r\) and \(s\) with transversal \(l\), the pairs are \(\angle3\) and \(\angle6\), \(\angle4\) and \(\angle5\)

Answer:

c. \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\)
d. Corresponding Angles Theorem
e. \(\angle3\) and \(\angle6\), \(\angle4\) and \(\angle5\)