Question

1. which step in the proof has a flaw? given ( overline{ab} cong overline{bc} ), prove b is the midpoint of ( overline{ac} )

Explanation:

To prove that \( B \) is the mid - point of \( \overline{AC} \), we need to show that \( \overline{AB}\cong\overline{BC} \) and \( B \) lies on \( \overline{AC} \). The given proof only mentions \( \overline{AB}\cong\overline{BC} \) (Step 1 is correct as it is given). But the definition of a mid - point (Step 2) requires the point to be collinear with the endpoints of the segment. Just because \( \overline{AB}\cong\overline{BC} \), we cannot assume \( B \) is on \( \overline{AC} \). For example, if \( A\), \( B\), and \( C\) form an isosceles triangle \( \triangle ABC\) with \( AB = BC\), \( B\) is not the mid - point of \( \overline{AC}\).

Answer:

Step 2