A congruence statement generally follows the syntax, "Shape ABCD is congruent to shape WXYZ." This notation convention matches the sides and angles of the two shapes; therefore, side AB of the first shape corresponds to side WX of the second one. Similarly, the angle BCD, or simply C, corresponds to the angle XYZ or Y.
The term "congruent" in geometry indicates that two objects have the same dimensions and shape. Although congruence statements are often used to compare triangles, they are also used for lines, circles and other polygons.
For example, a congruence between two triangles, ABC and DEF, means that the three sides and the three angles of both triangles are congruent.
- Side AB is congruent to side DE.
- Side BC is congruent to side EF.
- Side CA is congruent to side FD.
- Angle A is congruent to angle D.
- Angle B is congruent to angle E.
- Angle C is congruent to angle F.
By knowing some of these six congruences, it is possible to prove that two triangles are congruent and all six congruences are true.
This axiom states that if in triangles ABC and DEF, side AB is congruent to side DE, side AC is congruent to side DF and angle A is congruent to angle D, then the triangles are congruent.
If in triangles ABC and DEF, side AB is congruent to side DE, side BC is congruent to side EF and side CA is congruent to side FD, then the two triangles are congruent.
If in triangles ABC and DEF, angle A is congruent to angle D, angle B is congruent to angle E and side AB is congruent to side DE, then the two triangles are congruent.