Properties of congruence

The properties on congruence are the reflexive property, the symmetric property, and the transitive property.

Reflexive property

ABAB

∠A ≅ ∠A

Symmetric property

If ABCD, then CDAB

If ∠A ≅ ∠B , then ∠B ≅ ∠A

Transitive property

If ABCD and CDEF, then ABEF

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C


Naming the property of congruence that justifies each statement.



XYZW, then ZWXY     This is the symmetric property of congruence.

∠RTS ≅ ∠RTS    This is the reflexive property of congruence.

If GFST and STWU, then GFWU    This is the reflexive property of congruence.

A little exercise!

Try to complete each statement using the given property

Reflexive property of congruence

∠UGD ≅ ?

Symmetric property of congruence

If SEPO, then    ?    ≅    ?

Transitive property of congruence

If ∠S ≅ ∠T and ∠   ?   ≅ ∠U, then ∠   ?    ≅ ∠   ?



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