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 ${\displaystyle \triangle ABC}$ and ${\displaystyle \triangle DEF}$ such that their sides are equal, hence:

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

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