Exploring Congruency

When triangles are congruent, six facts are always true.

When triangles are congruent, one triangle can be moved (through one, or more, rigid motions) to coincide with the other triangle. All corresponding sides and angles will be congruent.

Consider the following two triangles:

Consider the following two triangles:

These two triangles are congruent:

KLM Corresponding sides are congruent: AB KL BC LM AC KM Corresponding angles are congruent: Angle A Angle K Angle B Angle L Angle C Angle M The good news is that when proving triangles congruent, it is not necessary to prove all six facts to show congruency. There are certain ordered combinations of these facts that are sufficient to prove triangles congruent. These combinations guarantee that, given these facts, it will be possible to construct triangles which will take on only one shape (be unique), thus insuring congruency.