Question

question 1 (1 point) determine whether the stated conclusion is valid based on the given information. if not, write invalid. explain your reasoning. given: if a point is the mid - point of a segment, then it divides the segment into two congruent segments. r is the mid - point of qs. conclusion: qr = rs a. valid; r is the mid - point of qs, so the hypothesis of the conditional is true, therefore the conclusion is true. the two congruent segments are qr and rs. b. invalid; the conclusion of the conditional statement is true, but that does not mean that the hypothesis is true. r may not be between q and s.

Explanation:

Step1: Recall mid - point definition

If a point \(R\) is the mid - point of a segment \(\overline{QS}\), by definition, it divides the segment into two congruent segments \(\overline{QR}\) and \(\overline{RS}\), i.e., \(\overline{QR}\cong\overline{RS}\).

Answer:

a. Valid; \(R\) is the mid - point of \(\overline{QS}\), so the hypothesis of the conditional is true, therefore the conclusion is true. The two congruent segments are \(\overline{QR}\) and \(\overline{RS}\).