Question

Rewrite the following conditional statement as a converse, inverse, and contrapositive: If two angles are supplementary, then one of the two angles is acute.

Answer 1

Part 1) The converse is "If one of the two angles is acute then two angles are supplementary"

Part 2) The inverse is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) The contrapositive is "If one of the two angles is not acute then two angles are not supplementary"

Explanation:

we have

The following conditional statement " If two angles are supplementary, then one of the two angles is acute"

The hypothesis is "If two angles are supplementary"

The conclusion is " one of the two angles is acute"

Part 1) Rewrite the conditional statement as a converse

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion

therefore

The converse of " If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is acute then two angles are supplementary"

Part 2) Rewrite the conditional statement as a inverse

we know that

To form the inverse of the conditional statement, negating both the hypothesis and conclusion of a conditional statement.

therefore

The inverse of " If two angles are supplementary, then one of the two angles is acute" is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) Rewrite the conditional statement as contrapositive

we know that

To form the contrapositive, switching the hypothesis and conclusion of a conditional statement and negating both

therefore

The contrapositive of "If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is not acute then two angles are not supplementary"