Let $ a, $ $ b $, and $ c $ be sides in a triangle, a $ h_a, $ $ h_b $, and $ h_c $ are the corresponding altitudes. Prove that $h ^ 2_a + h ^ 2_b + h ^ 2_c \leq \frac{3}{4} (a ^ 2 + b ^ 2 + c ^ 2). $ When is the equation valid?