Question

1. sp≅sq △spm≅△sqm any point on a bisector of a line segment is equidistant from the two endpoints of the line segment 6. lines drawn to endpoints of a segment are congruent sss congruence theorem corresponding parts of congruent triangles are congruent 7. 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¯. jamie made his first mistake in step 5. he used the statement he was trying to prove as a reason. jamie made his first mistake in step 6. the congruence statement should be that △spm is congruent to △qsm. jamie did not make any errors in his proof.

Explanation:

Step1: Analyze Step - 3 error

In geometry, just because a line is a bisector of a segment does not directly imply that the two sub - segments formed are congruent without additional information. Jamie cannot conclude that $\overline{MP}\cong\overline{MQ}$ just because line $MS$ is a bisector of $\overline{PQ}$.

Step2: Analyze Step - 5 error

The statement he used as a reason is incorrect. He should be using properties related to congruent triangles to prove congruence, not an incorrect or non - applicable statement.

Step3: Analyze Step - 6 error

The congruence statement should be based on correct application of congruence postulates or theorems. Since there were errors in previous steps, the congruence statement in Step 6 may be incorrect as well.

Answer:

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