Section 2.5 Congruence
¶One of the standard properties of Euclidean geometry is SAS congruence, which says that if two sides and the included angle match in two different triangles, then the triangles themselves are “the same”, that is, the triangles are congruent.
Although not a formal proof, we can illustrate SAS congruence by construction. That is, we start with an arbitrary triangle, then construct a new triangle so that two of its sides and the included angle are congruent to the corresponding parts of the original triangle. We then verify SAS congruence by measuring the remaining sides and angles in both triangles, and showing that these measurements match.
One such construction is shown in Figure 2.5.1.
Activity 2.5.1. Verifying SAS congruence.
Can you determine how the second triangle in Figure 2.5.1 was constructed?
The auxiliary objects used in the construction are shown in Figure 2.5.2.