Question

Jenni wrote a conditional statement and its converse. Conditional: If two angles are alternate interior angles, then they are congruent. Converse: If two angles are congruent, then they are alternate interior angles. Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.

Answer 1

Jenni did not write the converse statement properly. The converse of the conditional statement "If two angles are alternate interior angles, then they are congruent" should be "If two angles are congruent, then they are alternate interior angles."

To determine if the converse is true or false, we need to evaluate if it holds in all cases. In this case, the converse is false.

Counterexample: Consider two vertical angles. Vertical angles are congruent, but they are not alternate interior angles.

Therefore, the converse statement "If two angles are congruent, then they are alternate interior angles" is false, as shown by the counterexample of vertical angles.