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 $$\triangle ABC $$ and $$\triangle DEF $$ such that their sides are equal, hence:
 * 1) The angle $$\angle CAB $$ equals $$\angle FDE $$.(they have the same angle $$x $$)
 * 2) The angle $$\angle ABC $$ equals $$\angle DEF $$.(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.