Question

1. which lines, if any, must be parallel if ( mangle3 = mangle6 ) in the following picture? explain why.

a. ( rparallel s ), by the converse of the alternate interior angles theorem.
b. ( rparallel s ), by the converse of the alternate exterior angles theorem.
c. ( lparallel m ), by the converse of the alternate interior angles theorem.
d. ( lparallel m ), by the converse of the alternate exterior angles theorem.
e. no lines are parallel since there are no relationships in the angles.

Explanation:

• Identify the angles: $\angle3$ and $\angle6$ are alternate interior angles.
• Apply the theorem: The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.
• Determine the lines: The lines that are cut by the transversal to form $\angle3$ and $\angle6$ are lines $l$ and $m$.

Answer:

c. $l\parallel m$, by the Converse of the Alternate Interior Angles Theorem.