Please see the attached file for the fully formatted problems.
Let l, m, n be distinct lines and P, Q, R be distinct points. Prove the following:
(a) sigma l sigma m = sigma m sigma l if and only if l perpendicular to m.
(b) sigma p sigma m = sigma m sigma p if and only if P E m.
plus three more questions
Proofs involving reflections are provided. The solution is detailed and well presented.