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:
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.