Question

select the term that matches the statement numbered from the dropdown below, then determine the validity of the statement. if a point divides a segment into two equal halves, then it is a midpoint. a. if a point does not divide a segment into two equal halves, then it is not a midpoint. this is the contrapositive validity true b. if a point is not a midpoint, then it does not divide a segment into two equal halves. this is the inverse validity true c. if a point is a midpoint, then it divides a segment into two equal halves. this is the converse validity true

Explanation:

1. For a conditional statement "If \(p\), then \(q\)" (where \(p\) is the hypothesis and \(q\) is the conclusion):

• The contra - positive is "If not \(q\), then not \(p\)". Here, the original statement is "If a point divides a segment into two equal halves, then it is a mid - point". In option A, "If a point does not divide a segment into two equal halves, then it is not a mid - point" which is the contra - positive. The contra - positive of a true conditional statement is always true.
• The inverse is "If not \(p\), then not \(q\)". Option B "If a point is not a mid - point, then it does not divide a segment into two equal halves" is the inverse of the original statement. For a true conditional statement, the inverse is also true in this case as the definition of a mid - point is used.
• The converse is "If \(q\), then \(p\)". Option C "If a point is a mid - point, then it divides a segment into two equal halves" is the converse of the original statement. Since the definition of a mid - point implies this, the converse is true.

Answer:

A. Contrapositive, Validity: True
B. Inverse, Validity: True
C. Converse, Validity: True