AA Similarity

Theorem: Two triangles are similar if any two angles of one triangle are respectively equal to two angles of the other triangle.

Prerequisites:
AAA similarity (proof)
Angle sum property of triangle (proof)

Proof:

Let $\triangle ABC$ and $\triangle DEF$ be two triangles such that $\angle A = \angle D$ and $\angle B = \angle E$.
By using angle sum property of triangles,

$\qquad\quad\begin{align}\angle C &= 180^o - \angle A - \angle B\\
&= 180^o - \angle D -\angle E\qquad\qquad\text{(given)}\\
&= \angle F\end{align}$

Hence, all the three pair of angles are congruent. Thus,  $\triangle ABC\sim\triangle DEF$  by AAA similarity.


Recommended:
SSS similarity
Midpoint Theorem
Angle Bisector Theorem