Question

1. 6. △spm≅△sqm 6. sss congruence theorem any point on a bisector of 7. a line segment is equidistant from the two endpoints of the line segment 7. corresponding parts of congruent triangles are congruent which statement best describes jamies proof? a jamie made his first mistake in step 3. he cannot conclude that mp is congruent to mq based on the fact that line ms is a bisector of pq. b jamie made his first mistake in step 5. he used the statement he was trying to prove as a reason. c jamie made his first mistake in step 6. the congruence statement should be that △spm is congruent to △qsm. d jamie did not make any errors in his proof.

Explanation:

A line - segment bisector divides a line segment into two equal parts. Just because a line is a bisector of a segment doesn't mean that any point on it is equidistant from the endpoints of the bisected segment. In step 3, Jamie wrongly assumed that since \(MS\) is a bisector of \(PQ\), \(MP\cong MQ\). The correct property of a bisector is that it divides the segment into two equal - length sub - segments, not that points on the bisector are equidistant from the endpoints.

Answer:

A. Jamie made his first mistake in Step 3. He cannot conclude that \(MP\) is congruent to \(MQ\) based on the fact that line \(MS\) is a bisector of \(PQ\).