Example of Angle Side Angle Proof
These two triangles are congruent because 2 angles and the included side are congruent.
$$ \triangle ABC \cong \triangle XYZ $$
$
\begin{aligned}
\angle CAB \cong \angle ZXY
\\
\overline{AB} \cong \overline{ XY}
\\
\angle ACB \cong \angle XZY
\end{aligned}
$
Why it Makes sense
Consider the two partially drawn triangles below. At the start of the animation you can see that both triangles have a congruent side that is included between two congruent angles. In both triangles, we are locked into those congruent pieces. There is only 1 way to complete these triangles, and in both cases the resultant triangle must have the same measurements, which the demonstration below shows.
