Question

1. refer to the diagram below. given that l || m, correctly classify ∠6 and ∠8 and decide whether they are congruent or supplementary.

a. alternate interior angles; congruent
b. alternate exterior angles; congruent
c. vertical angles; congruent
d. corresponding angles; congruent
e. interior angles on the same side of the transversal; supplementary

1. refer to the diagram above. given that l || m, correctly classify ∠4 and ∠5 and decide whether they are congruent or supplementary.

a. alternate interior angles; congruent
b. alternate exterior angles; congruent
c. vertical angles; congruent
d. corresponding angles; congruent
e. interior angles on the same side of the transversal; supplementary

1. if ____, then either a or b may be substituted for the other in any equation.

a. a = b
b. a ≠ b
c. a < b
d. a = a
e. a > b

1. if two parallel lines are cut by a transversal, then their alternate exterior angles are ____.

a. supplementary
b. adjacent
c. congruent
d. a linear pair
e. complementary

1. if the exterior sides of ____ angles are perpendicular, then the angles are complementary.

a. corresponding
b. adjacent
c. alternate exterior
d. vertical
e. alternate interior

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines \(l\) and \(m\) are cut by a transversal \(n\), different angle - pair relationships exist.

Step2: Analyze \(\angle6\) and \(\angle8\) in question 9

\(\angle6\) and \(\angle8\) are vertical angles. By the vertical - angles theorem, vertical angles are congruent.

Step3: Analyze \(\angle4\) and \(\angle5\) in question 10

\(\angle4\) and \(\angle5\) are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent.

Step4: Recall substitution property in question 11

If \(a = b\), then \(a\) and \(b\) are equal and can be substituted for each other in any equation.

Step5: Recall properties of alternate exterior angles in question 12

When two parallel lines are cut by a transversal, alternate exterior angles are congruent.

Step6: Recall angle - relationship for perpendicular exterior sides in question 13

If the exterior sides of adjacent angles are perpendicular, then the angles are complementary.

Answer:

1. C. Vertical angles; congruent
2. A. Alternate interior angles; congruent
3. A. \(a = b\)
4. C. congruent
5. B. adjacent