Question

drag each statement below to the original conditional, converse, biconditional, inverse, or contrapositive category.
original conditional: no answers chosen
converse: no answers chosen
biconditional: no answers chosen
inverse: no answers chosen
contrapositive: no answers chosen
possible answers:
if the angles are supplementary, then their sum is 180°.
if the angles do not sum to 180°, then they are not supplementary.
if the angles are not supplementary, then their sum is not 180°.
if the angles sum to 180°, then they are supplementary.
angles are supplementary if and only if they sum to 180°.

Explanation:

Step1: Recall conditional statement forms

Let the original conditional statement be "If \(p\), then \(q\)" where \(p\) is the hypothesis and \(q\) is the conclusion.

Step2: Identify original conditional

The original conditional statement about supplementary - angle definition is "If the angles are supplementary, then their sum is 180°".

Step3: Find the converse

The converse of "If \(p\), then \(q\)" is "If \(q\), then \(p\)". So the converse is "If the angles sum to 180°, then they are supplementary".

Step4: Find the inverse

The inverse of "If \(p\), then \(q\)" is "If not \(p\), then not \(q\)". So the inverse is "If the angles are not supplementary, then their sum is not 180°".

Step5: Find the contra - positive

The contra - positive of "If \(p\), then \(q\)" is "If not \(q\), then not \(p\)". So the contra - positive is "If the angles do not sum to 180°, then they are not supplementary".

Step6: Find the biconditional

The biconditional is "Angles are supplementary if and only if they sum to 180°".

Answer:

Original Conditional: If the angles are supplementary, then their sum is 180°.
Converse: If the angles sum to 180°, then they are supplementary.
Inverse: If the angles are not supplementary, then their sum is not 180°.
Contrapositive: If the angles do not sum to 180°, then they are not supplementary.
Biconditional: Angles are supplementary if and only if they sum to 180°.