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What is perpendicular axes theorem?

Theorem of Perpendicular Axis:
       It states that moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of its moment of inertia about the two mutually perpendicular axes lying in its plane, intersecting at that point through which the third axis is passing.
                                                 

Proof: Consider a mass particle P of mass mi of the plane lamina at a perpendicular distance of r_i from z – axis. Let the perpendicular distance from P to x – axis be x_i and from P to y – axis be y_i.
                                                 
From the definition of moment of inertia,