Sides of Orthic triangle DEF are anti parallel to ABC

If D,E,F are the feet of altitudes from A,B,C to BC,CA,AB then sides of DEF are anti parallel to ABC.
What does it mean?

Let's focus on BCEF quadrilateral which is cyclic.
Angle AEF = B and angle AFE = C.
If these angles were swapped then EF would be || to BC. But since they are in the exact opposite order it's called anti parallel.
Same can be shown for other sides.

Also in the triangle DEF, extending the argument above:
Angle D = 180 - 2A
Angle E = 180 - 2B
Angle F = 180 - 2C

Assuming that ABC is an acute angle triangle.

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