Question

use the given information to determine which lines, if any, are parallel. justify each conclusion with a theorem.
∠3≅∠8
determine the pair of parallel lines and justify the conclusion. select all that apply.
a. b||m by the alternate interior angles theorem
b. a||n by the same - side interior angles theorem
c. n||m by the corresponding angles theorem
d. a||b by the alternate exterior angles theorem
e. there is not enough information to prove whether or not any of the lines are parallel.

Explanation:

The Alternate Interior Angles Theorem involves angles between two lines and a transversal inside the two - lines. The Same - Side Interior Angles Theorem involves angles on the same side of the transversal inside the two lines. The Corresponding Angles Theorem involves angles in the same relative position with respect to the transversal and the two lines. The Alternate Exterior Angles Theorem involves angles outside the two lines and on opposite sides of the transversal. Given \(\angle3\cong\angle8\), these angles are not related in a way that satisfies any of the parallel - line theorems for the given pairs of lines in options A - D.

Answer:

E. There is not enough information to prove whether or not any of the lines are parallel