Square $ABCD$ of area $9$ cm² has the largest possible equilateral triangle inscribed in it. The triangle has vertices $A$, $E$, and $F$, where E is between $B$ and $C$, and $F$ is between $C$ and $D$.

1. Why is $ΔADF ≅ ΔABE$?

   Hint (a):

   In answering these questions, think about the degree measures of the angles.
   Label the interior angles of the equilateral triangle.

   Angles (a):

2. Why is $ΔCEF$ isosceles?

   Hint (b):

   Find and label the base angles of the isosceles triangle.

   Base Angles (b):

3. Find the area of triangle $AEF$.

   Hint (c):

   Find the angles in triangle $AEF$. Then use a trig function to find a side of the equilateral triangle.
   Then find the height of the equilateral triangle. At that point, you can use the formula: $.5(\text{base})(\text{height})$.