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.
PROPERTIES
OF CONGRUENCE
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Reflexive Property |
For all angles , . An angle is congruent to itself. |
These
three properties define an
equivalence relation
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Symmetric Property |
For any angles , if , then . Order of congruence does not matter. |
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Transitive Property |
For any angles , if and , then . If two angles are both congruent to a third angle, then the first two angles are also congruent. |