Geometry for Elementary School/The Angle-Side-Angle congruence theorem

In this chapter, we will discuss another congruence theorem, this time the Angle-Side-Angle theorem, usually shortened as ASA. The side in this theorem is called the included side.

The Angle-Side-Angle congruence theorem

Given two triangles $\mathrm{△}ABC$ and $\mathrm{△}DEF$ such that their sides are equal, hence:

1. The angle $\mathrm{\angle }BAC$ equals $\mathrm{\angle }EDF$.
2. The side $\overline{BA}$ equals $\overline{ED}$.
3. The angle $\mathrm{\angle }ABC$ equals $\mathrm{\angle }DEF$ (These are the angles between the sides, or the included angle).

Then the triangles are congruent and their other angles and sides are equal too. Note that the side must be the included side of the two angles.