Question

What is the contrapositive of the following statement?

If M is the midpoint of PQ, then PM is congruent to OM.
If M is the midpoint of PO, then PM is congruent to OM.
If PM is congruent to OM, then M is the midpoint of PO.
If M is not the midpoint of PQ, then PM is not congruent to QM.
If PM is not congruent to OM, then M is not the midpoint of PQ

Answer 1

If M is not the midpoint of , then is not congruent to

Explanation:

Answer 2

For the statement;

If M is the midpoint of
`\overline{PQ}`, then
`\overline{PM}` is congruent to
`\overline{QM}`

The contrapositive statement is therefore;

If M is not the midpoint of
`\overline{PQ}`, then
`\overline{PM}` is not congruent to
`\overline{QM}`

Explanation:

Contraposition in logic describes the transitioning from an implication/conditional statement into its equivalent contrapositive

The contrapositive of the statement p → q is equal to ~p → ~q

Therefore, the contrapositive of a conditional or implication statement is equivalent, logically to the original statement