Question

1. sara is trying to justify a step in her paragraph proof. what is the property that she should use?

\\( \overline { a b } \cong \overline { b c } , \overline { b c } \cong \overline { x y } \\), therefore \\( \overline { a b } \cong \overline { x y } \\)
symmetric property of congruence
equality of congruence property
reflexive property of congruence
transitive property of congruence

Explanation:

The Transitive Property of Congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\). In this case, \(\overline{AB}\cong\overline{BC}\) and \(\overline{BC}\cong\overline{XY}\), so by the Transitive Property of Congruence, \(\overline{AB}\cong\overline{XY}\).
The Symmetric Property of Congruence is \(a\cong b\) implies \(b\cong a\). The Reflexive Property of Congruence is \(a\cong a\). There is no “Equality of Congruence Property” in standard congruence properties.

Answer:

Transitive Property of Congruence