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Properties of Congruence

Rule

Properties of Congruence

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

Rule

Reflexive Property of Congruence

Any geometric figure is congruent to itself. For example, the segment AB\overline{AB} is always congruent with itself. AB AB \overline{AB}\ \cong\overline{AB}

Rule

Symmetric Property of Congruence

If a given geometric object, A,A, is congruent with another geometric object, B,B, then BB is also congruent with A.A. For example, if triangle AA is congruent with triangle B,B, then BB is also congruent with A.A. ABthenBA \triangle A \cong \triangle B \quad\text{then} \quad \triangle B \cong \triangle A

Rule

Transitive Property of Congruence

If geometric objects AA and BB are congruent and BB is also congruent with C,C, then AA is congruent with C.C. If AB and BC, then AC \text{If }\angle A\cong\angle B\ \text{and}\ \angle B\cong\angle C,\ \text{then}\ \angle A\cong\angle C In this example, angles AA and CC are congruent because A\angle A is congruent with B\angle B and B\angle B is congruent with C.\angle C.