152k views
3 votes
Write the converse of this conditional. Then determine if the converse is true. If it isn't, provide a counterexample.

If a polygon is a pentagon, then it has five sides.

User Hazonko
by
8.3k points

1 Answer

4 votes

To write the converse of a conditional, switch the hypothesis and the conclusion. You may need to adjust the language a little.

Conditional:

If a polygon is a pentagon, then it has five sides.

The hypothesis is "a polygon is a pentagon."

The conclusion is "it has five sides."

Now switch the hypothesis and the conclusion and adjust the language a little.

Converse:

If a polygon has five sides, then it is a pentagon.

As you can see, the hypothesis and conclusion were switched to form the converse.

Every five-sided polygon is a pentagon, and every pentagon is a five-sided polygon, so both the conditional and the converse are true.

User Sez
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories