Question

parallel lines and their angles: theorems (p→q) and their converse (q→p) 1. if p→q, what is the converse? corresponding angles theorem: if two parallel lines are cut by a transversal, then the corresponding angles are congruent. corresponding angles converse if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. alternate interior angles theorem: if two parallel lines are cut by a transversal, then the alternate interior angles are congruent. alternate interior angles converse if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. alternate exterior angles theorem: if two parallel lines are cut by a transversal, then the alternate interior angles are congruent. alternate exterior angles converse if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. consecutive interior angles theorem: if two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary. consecutive interior angles converse if two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. transitive property of parallel lines if two lines are parallel to the same line, then they are parallel to each other.

Explanation:

The converse of a conditional statement \(p
ightarrow q\) is formed by reversing the hypothesis \(p\) and the conclusion \(q\). So, if the original statement is "if \(p\), then \(q\)" (\(p
ightarrow q\)), its converse is "if \(q\), then \(p\)" (\(q
ightarrow p\)).

Answer:

\(q
ightarrow p\)