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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? Give a counterexample to dispute the validity of the converse statement

2 Answers

3 votes

Answer: Corresponding Angles

Step-by-step explanation:

Took it on the test!

User John Kalberer
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Final answer:

Jenni correctly wrote the converse of the conditional statement structurally, but the converse is not necessarily true. Angles can be congruent without being alternate interior angles.

Step-by-step explanation:

Jenni wrote the conditional statement: If two angles are alternate interior angles, then they are congruent. The converse of this statement would be: If two angles are congruent, then they are alternate interior angles. Jenni's converse statement is logically correct in its structure; however, it is not necessarily true in geometry.

While alternate interior angles are indeed congruent when two lines are crossed by a transversal and the lines are parallel, just because two angles are congruent does not mean they have to be alternate interior angles. A counterexample could be two congruent angles that are both located at the corners of two separate squares. These congruent angles are not alternate interior angles since they are not formed by a transversal intersecting parallel lines.

User Tejesh Alimilli
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