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

 Geometry for Elementary School The Angle-Side-Angle congruence theorem The Side-Angle-Angle congruence theorem The Right angle-Hypotenuse-Side 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 ${\displaystyle \triangle ABC}$  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.