AA similarity criterion is extended to AAA criterion using ______

AA similarity criterion is extended to AAA criterion using Angle sum property of a triangle.

Let us consider the triangles to be $∆ABC$ and $∆XYZ$ and let the two corresponding equal angles be $\angle A=\angle X and \angle B=\angle Y,\Rightarrow \angle A+\angle B=\angle X+\angle Y$...(1)

Now, In $∆ABC$ and $∆XYZ$, according to angle sum property of a triangle

$\angle A+\angle B+\angle C=180$ and $\angle X+\angle Y+\angle Z=180$

$\Rightarrow \angle C=180-\left(\angle A+\angle B\right) and \angle Z=180-\left(\angle X+\angle Y\right)$

$\therefore \angle C=\angle Z$   (Using 1)

Therefore, AA similarity criterion is extended to AAA criterion using Angle sum property of a triangle.