Question

1. which step in the proof has a flaw?

given: \\( \overline { a b } \cong \overline { c d } \\) and \\( \overline { c d } \cong \overline { e f } \\)
prove: \\( \overline { a b } \cong \overline { e f } \\)

1. \\( \overline { a b } \cong \overline { c d } \\) and \\( \overline { c d } \cong \overline { e f } \\) 1) given
2. \\( \overline { a b } \cong \overline { e f } \\) 2) symmetric property of congruence

Explanation:

Step1: Recall the properties of congruence

The symmetric property of congruence states that if \( \overline{AB}\cong\overline{CD}\), then \( \overline{CD}\cong\overline{AB}\). The transitive property of congruence states that if \( \overline{AB}\cong\overline{CD}\) and \( \overline{CD}\cong\overline{EF}\), then \( \overline{AB}\cong\overline{EF}\).

Step2: Analyze the given proof

In the given proof, from \( \overline{AB}\cong\overline{CD}\) and \( \overline{CD}\cong\overline{EF}\), we should use the transitive property (not the symmetric property) to conclude \( \overline{AB}\cong\overline{EF}\).

Answer:

Step 2 has a flaw. The reason should be the transitive property of congruence, not the symmetric property of congruence.