Question

#2
match the conditional statement p→q, the converse q→p, the inverse ~p→~q, and the contrapositive ~q→~p in words.
let p be “two angles are supplementary” and let q be “the measures of the angles sum to 180°”
the conditional statement p→q
the converse q→p
the inverse ~p→~q
the contrapositive ~q→~p
:: if the measures of two angles do not sum to 180°, then they are not supplementary.
:: if the measures of two angles sum to 180°, then they are not supplementary.
:: if the two angles are not supplementary, then their measures do not sum to 180°.
:: if the measures of two angles sum to 180°, then they are supplementary.
:: if two angles are not supplementary, then the measures of the angles sum to 180°.

Explanation:

1. The conditional statement \(p

ightarrow q\) means if \(p\) is true, then \(q\) is true. Here, \(p\) is "two angles are supplementary" and \(q\) is "the measures of the angles sum to 180°", so \(p
ightarrow q\) is "If two angles are supplementary, then the measures of the angles sum to 180°".

1. The converse \(q

ightarrow p\) swaps the hypothesis and conclusion. So it is "If the measures of two angles sum to 180°, then they are supplementary".

1. The inverse \(\sim p

ightarrow\sim q\) negates both \(p\) and \(q\). So it is "If two angles are not supplementary, then the measures of the angles do not sum to 180°".

1. The contra - positive \(\sim q

ightarrow\sim p\) negates and swaps \(p\) and \(q\). So it is "If the measures of two angles do not sum to 180°, then they are not supplementary".

Answer:

• The conditional statement \(p

ightarrow q\): If two angles are supplementary, then the measures of the angles sum to 180°.

• The converse \(q

ightarrow p\): If the measures of two angles sum to 180°, then they are supplementary.

• The inverse \(\sim p

ightarrow\sim q\): If two angles are not supplementary, then the measures of the angles do not sum to 180°.

• The contra - positive \(\sim q

ightarrow\sim p\): If the measures of two angles do not sum to 180°, then they are not supplementary.