In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B. Show that
(i) `triangleAMC ~= triangleBMD`
(ii) `angleDBC` is a right angle.
(iii) `triangleDBC ~= triangleACB`
(iv) `CM = 1/2 AB`