How Many Sides For Similarity?
In the figure above, \(\angle A\cong\angle F\), \(\angle B\cong\angle G\), \(\angle C\cong\angle H\), \(\angle D\cong\angle I\), and \(\angle E\cong\angle J\).
You may set any side length in pentagon \(FGHIJ\) to be whatever value you want. Your goal is to make the pentagons similar.
What is the minimum number of sides needed in order for both pentagons to always be similar?