Question

question 3.
given the conditional statement
if two lines that are cut by a transversal are parallel, then consecutive exterior angles are supplementary
in each case, determine whether the given statement is the converse or the inverse of the given conditional statement. if it is necessary, select neither
if two lines that are cut by a transversal are parallel, then consecutive exterior angles are not supplementary
if two lines cut by a transversal are not parallel, then consecutive exterior angles are not supplementary

Explanation:

Let the original conditional statement be \(p
ightarrow q\), where \(p\): "two lines that are cut by a transversal are parallel" and \(q\): "consecutive exterior angles are supplementary".

The inverse of \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\).

For the first statement: "If two lines that are cut by a transversal are parallel, then consecutive exterior angles are not supplementary", it is not in the form of inverse (\(
eg p
ightarrow
eg q\)) or converse (\(q
ightarrow p\)).

For the second statement: "If two lines cut by a transversal are not parallel (\(
eg p\)), then consecutive exterior angles are not supplementary (\(
eg q\))", it is in the form of \(
eg p
ightarrow
eg q\) which is the inverse of the original statement \(p
ightarrow q\).

Answer:

First statement: neither; Second statement: inverse.