Question

Name the property that the statement illustrates.

Answer 1

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.

Answer 2

Answer:

Transitive property of segment congruence

Step-by-step 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 $a=c$.