Firstly,It is not for all reaction turbines.It is true only for a Parsons reaction turbine having degree of Reaction 0.5.

Next the enthalpy drop in moving blades expressed in terms of increase in Kinetic energy change(relative velocity component) and enthalpy drop in Fixed blade when expressed in inlet absolute Velocity terms are made equal for Parsons.

This condition satisfies only when the triangles are similar triangles leading to answer to your question.

For derivation pl refer to any standard Text book.