Question

question 1-4
determine whether the conditional and its converse are both true. if both are true, combine them as a biconditional. if either is false, give a c
conditional: if two co - planar lines are parallel, they do not intersect.
converse: if two co - planar lines do not intersect, they are parallel.

one statement is false. if two co - planar lines do not intersect, they could be skew.
one statement is false. if two co - planar lines are parallel, they may intersect twice.
both statements are true. two co - planar lines are parallel if and only if they do not intersect.
both statements are true. two co - planar lines are not parallel if and only if they do not intersect.

Explanation:

The conditional ("If two co-planar lines are parallel, they do not intersect") is true by definition of parallel lines. The converse ("If two co-planar lines do not intersect, they are parallel") is also true because non-intersecting co-planar lines are parallel (skew lines are non-co-planar, so they don’t apply here). Thus, combining them into a biconditional is valid.

Answer:

Both statements are true. Two co-planar lines are parallel if and only if they do not intersect.