Kristen H.
asked • 02/09/17
Conditional: If point M is the midpoint of segment AB, then point M is between points A and B.
For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply.
ConditionalConverseInverse
Contrapositive
2 Answers By Expert Tutors
Doug C. answered • 02/09/17
Math Tutor with Reputation to make difficult concepts understandable
The converse of p->q is q->p. For this case: if M is between points A and B, then M is the midpoint of seg AB.
False as illustrated by: A-----M--------------B
The inverse is represented by not p -> not q. If M is not the midpoint of seg AB, then M is NOT between A and B.
False: A-------------------M----B
Contrapositive: not Q -> not P. If M is not between A and B, then M is not the midpoint of seg AB.
True: M----A-------B. If M is not between it for sure cannot be the midpoint.
The contrapositive of an implication/conditional is always logically equivalent to the original.
If the conditional is true, the converse it not necessarily true. And in this case it is false.
The inverse is false, the point can be not a midpoint and be between.
The contrapositive is always true.
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We don’t have your requested question, but here is a suggested video that might help.
Which statement is the converse of the conditional statement: If point B bisects line segment AC into two congruent segments, then point B is the midpoint: If point B does not bisect line segment AC into two congruent segments, then point B is not the midpoint If point B is the midpoint, then point B bisects line segment AC into two congruent segments_ If point B is not the midpoint, then point B does not bisect line segment AC into two congruent segments_ Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint