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Given m parallel to n; <1 congruent <3, prove l parallel m.

a) l is parallel to n
b) l is congruent to n
c) l is congruent to m
d) l is parallel to m

1 Answer

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Final answer:

To prove that line l is parallel to line m, we rely on the Alternate Interior Angles Converse theorem. The congruence of angles <1 and <3 suggests that l and m are parallel, determining that option d is the correct answer.

Step-by-step explanation:

The question involves proving that line l is parallel to line m, given that line m is parallel to line n, and that <1 is congruent to <3. If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel by the Alternate Interior Angles Converse theorem. Since m is given as parallel to n, and the congruence of angles 1 and 3 indicates they are alternate interior angles with respect to the transversal cutting lines m and n, line l, which also forms these congruent alternate interior angles, must be parallel to line m. Therefore, option d (l is parallel to m) is the correct answer.

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