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

Explanation:

Step1: Analyze the Conditional Statement

The conditional statement is "If two co - planar lines are parallel, they do not intersect." By the definition of parallel lines in a plane, parallel lines never meet (intersect). So this statement is true.

Step2: Analyze the Converse Statement

The converse statement is "If two co - planar lines do not intersect, they are parallel." In a plane, two non - intersecting lines are parallel (this is the property of lines in a plane: the only two possibilities for two co - planar lines are that they are parallel or they intersect). So this statement is also true.

Step3: Determine the Biconditional

Since both the conditional and its converse are true, the biconditional is "Two co - planar lines are parallel if and only if they do not intersect."

Answer:

The correct option is "Both statements are true. Two co - planar lines are parallel if and only if they do not intersect." (the fourth option in the list of choices)