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

In this chapter, we will discuss yet another congruence theorem, the Side-Angle-Angle congruence theorem, usually abbreviated as SAA(or AAS - Angle-Angle-Side , commonly used in India)

The Angle-Side-Angle congruence theorem

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

1. The angle $\mathrm{\angle }CAB$ equals $\mathrm{\angle }FDE$.(they have the same angle $x$)
2. The angle $\mathrm{\angle }ABC$ equals $\mathrm{\angle }DEF$.(they have the same angle $z$)
3. The side $\overline{BC}$ equals $\overline{EF}$.(they have the same side $y$)

Then the triangles are congruent and their other angles and sides are equal too.