Question

Name the property that the statement illustrates.

Answer 1

Transitive property of segment congruence

Explanation:

The reflexive, symmetric, and transitive properties are the criterion for an equivalence relation. In terms of congruence,

• The reflexive property states that
  `\overline{XY} \cong \overline{XY}` (a segment is congruent to itself)
• The symmetric property states that if
  `\overline{AB} \cong \overline{CD}`, then
  `\overline{CD} \cong \overline{AB}` (this is essentially commutativity)
• The transitive property states that if
  `\overline{AB} \cong \overline{CD}` and
  `\ovelrine{CD} \cong \overline{EF}`, then
  `\overline{AB} \cong \overline{EF}`.

In terms of general equivalence relations,

• The reflective property states that
  `a = a`.
• The symmetric property states that if
  `a=b`, then
  `b=a`.
• The transitive property states that if
  `a=b` and
  `b=c`, then
  `a=c`.

Answer 2

That's the transitive property.

The fact that congruence is transitive means exactly what you have written: if A is congruent to B and B is congruent to C, then you can "bridge" from A to C.