Question

1. which step in the proof has a flaw? given ( overline{ab} cong overline{bc} ), prove b is the midpoint of ( overline{ac} ) step 1 ( overline{ab} cong overline{bc} ) given step 2 b is the midpoint of ( overline{ac} ) definition of midpoint step 3 qed step 3 no flaw. step 1 step 2

Explanation:

Step1: Analyze the definition of a midpoint

A midpoint \( B \) of a segment \( \overline{AC} \) requires that \( AB = BC \) and \( B \) lies on \( \overline{AC} \).

Step2: Check the given proof

The proof only uses \( \overline{AB}\cong\overline{BC} \) (which means \( AB = BC \) in length) but does not mention that \( B \) is on \( \overline{AC} \). Just having \( \overline{AB}\cong\overline{BC} \) is not sufficient to conclude \( B \) is the mid - point of \( \overline{AC} \) (for example, if \( A\), \( B\), \( C\) form a triangle, \( B \) is not a mid - point of \( AC \)). So, step 2 has a flaw.

Answer:

Step 2