Rotational Motion Part 1

By perpendicular axes theorem,
Ix=Ix+Iy‌‌ or,‌‌Iz=2Iy
( as Ix=Iy by symmetry of the figure)
∴IEF=‌

Iz

2

....(i)
By perpendicular axes theorem,
Iz=IAC+IBD=2IAC
(As IAC=IBD by symmetry of the figure)
∴IAC=‌

Iz

2

....(ii)
From (i) and (ii), we get IEF=IAC.