What is Congruence?
Two geometrical figures are said to be congruent if they are identical in every respects.
For example, two squares of the same side-length are congruent, as shown below:
Similarly, two circles with the same radius are congruent:
If two geometrical figures are congruent, they can be exactly superimposed upon each other.
✍Note: If a figure \(A\) is congruent to a figure \(B\), we will write this fact as follows: \(A \cong B\)\. Notice the following obvious facts about congruence:
If \(A \cong B\), then \(B \cong A\). This simply means that saying that \(A\) is congruent to \(B\) is the same as saying that \(B\) is congruent to \(A\).
If \(A \cong B\) and \(B \cong C\), then \(A \cong C\). This should once again be easy to understand. If \(A\) is congruent to \(B\), it can be superimposed exactly on \(B\). Similarly, \(B\) can be superimposed exactly on \(C\). Thus, \(A\) can be superimposed exactly on \(C\), and hence \(A \cong C\).