Question

consider the conditional statement: if two parallel lines are cut by a transversal, then the corresponding angles are congruent. fill in the blanks to write the converse of this statement. if two lines are cut by a transversal such that
_______________________________,
then _______________________________.

Explanation:

Step1: Recall converse definition

The converse of a conditional statement "if p then q" is "if q then p".

Step2: Identify p and q in original statement

In "If two parallel lines are cut by a transversal, then the corresponding angles are congruent", p is "two parallel lines are cut by a transversal" and q is "the corresponding angles are congruent".

Step3: Write the converse

We swap p and q.

Answer:

If two lines are cut by a transversal such that the corresponding angles are congruent, then the two lines are parallel.