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Properties of Congruence

The following are the properties of congruence . Some textbooks list just a few of them, others list them all. These are analogous to the properties of equality for real numbers. Here we show congruences of angles , but the properties apply just as well for congruent segments , triangles , or any other geometric object.

Reflexive Property

For all angles A , A A .

An angle is congruent to itself.

These three properties define an equivalence relation


Symmetric Property

For any angles A and B ,

if A B , then B A .

Order of congruence does not matter.

Transitive Property

For any angles A , B , and C ,

if A B and B C , then A C .

If two angles are both congruent to a third angle, then the first two angles are also congruent.