Chapter 1.8, Problem 6PSB

To determine

To write down the converse, the inverse, and the contrapositive of statement and determine whether that statement is true or false.

Answer to Problem 6PSB

Converse of a statement is False. Inverse of statement is False. Contrapositive of a statement is True.

Explanation of Solution

Given information:

  $Thegivenstatementis“IfMisthemidpointof\overline{AB},thenM,A,andBarecollinear.”$

Every conditional statement “If p, then q” has three other statements associated with it.

  $Aconverse\left(Ifq,thenp.\right)$

  $Aninverse(If~p,then~q.)$

  $Acontrapositive(If~q,then~p.)$

By referring to above associated statements, we can write:

Converse: If M, A, and B are collinear, then M is the mid-point of $\overline{AB}$

Inverse: If M is not the mid-point of the $\overline{AB}$ , then M, A, and B are non-collinear.

Contrapositive: If M, A, and B are non-collinear, then M is not the mid-point of the $\overline{AB}$ .

If points are collinear, they lie on same straight line. If M, A, and B are collinear, then M not necessary to be the mid-point of $\overline{AB}$ . It may be the mid-point or not be the mid-point of $\overline{AB}$ .

Non collinear points don’t lie on same straight line. A point cannot be mid-point if it is not on a straight line.