Question

1. which step in the proof has a flaw?

given: rs = 8 and xy = 8
prove: \\( \overline { r s } \cong \overline { x y } \\)

statement

1. rs = 8 and xy = 8
2. rs = xy
3. \\( \overline { r s } \cong \overline { x y } \\)

reason

1. given
2. reflexive property of equality
3. definition of congruence

statement 2
reason 2
statement 3
reason 3

Explanation:

Step1: Recall the properties of equality

The reflexive property of equality states that \(a = a\). But here, we have \(RS = 8\) and \(XY = 8\), so \(RS=XY\) by the transitive property of equality (\(a = c\) and \(b = c\) implies \(a = b\)), not the reflexive property.

Step2: Analyze each step

• Step 1: Correct as it is given.
• Step 2: The reason (reflexive property) is wrong.
• Step 3: If \(RS = XY\), then \(\overline{RS}\cong\overline{XY}\) by the definition of congruence (segments with equal lengths are congruent), so statement 3 and reason 3 are correct.

Answer:

Reason 2