Theorem 4.9: If R is a reflection, then R(R(A)) = A for all points A in the plane.

Proof: Let F be the foot of the point A in the line about which the plane is reflected. By Theorem 4.6,

R(A) = 2F - A

so

R(R(A)) = 2F - (2F - A) = A

next theorem (4.10)