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elaineandrei93

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

In terms of general equivalence relations,

  • The reflective property states that [tex]a = a[/tex].
  • The symmetric property states that if [tex]a=b[/tex], then [tex]b=a[/tex].
  • The transitive property states that if [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex].
ChefTopeau

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.

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