To prove that angle FAG is half of a right angle, we first need to establish the following facts:

Since ABCD is a square, all angles are right angles.AE is cut off equal to AB, which means AE = AB. Thus, AECD is a square as well.AFCG is a rectangle formed by extending FC to G, because AF is perpendicular to CG and FG.

Now, let's focus on triangle FAG:

In rectangle AFCG, angle AFG is a right angle because AF is perpendicular to CG.In square AECD, angle DAC = angle DCA = 45°.Since AE = AB, triangle ABE is isosceles, which means angle ABE = angle AEB = 45°.

Now, angle FAG can be expressed as:
angle FAG = angle DAE + angle ABE = 45° + 45° = 90°

Therefore, angle FAG is half of a right angle.