Theorem 4.4: If we compose two isometries, the result is an isometry.

Proof: Let M1 and M2 be the two isometries. Let A and B be two points in the plane. Then

|M2(M1(A), M2(M1(B)|

= |M1(A), M1(B)|

= |A, B|

next theorem (4.5)