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Geometry 13 Online
OpenStudy (anonymous):

Given ΔLMN where the length of segment NP is greater than the length of segment LP, the following is an indirect paragraph proof proving segment MP is not a median: Triangle LMN is shown with point P on side LN. A segment is drawn between points M and P. Assume segment MP is a median. According to the definition of a median, point P is the midpoint of side L N. By the definition of a midpoint NP = LP. This contradicts the given statement. Therefore, segment MP is not a median. Is the indirect proof logically valid? If so, why? If not, why not?

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