# How Many Sides For Similarity?

Geometry Level 4

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?

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