Question

1. $overline{sp}congoverline{sq}$ 5. lines drawn to endpoints of a segment are congruent
2. $\triangle spmcong\triangle sqm$ 6. sss congruence theorem
3. any point on a bisector of 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 $overline{mp}$ is congruent to $overline{mq}$ based on the fact that line $ms$ is a bisector of $overline{pq}$.
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 $\triangle spm$ is congruent to $\triangle qsm$.
d jamie did not make any errors in his proof.

Explanation:

In a proof, one cannot use the statement to be proven as a reason. In Step 5, the statement $\overline{SP}\cong\overline{SQ}$ is likely what Jamie is trying to prove in the overall context, yet he uses "Lines drawn to endpoints of a segment are congruent" which is circular - reasoning if this is the statement to be proved.

Answer:

B. Jamie made his first mistake in Step 5. He used the statement he was trying to prove as a reason.