In right triangle ABC right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and

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 (see the given figure). Show that:
(i) ΔAMC ≅ ΔBMD
(ii) ∠DBC is a right angle.
(iii) ΔDBC ≅ ΔACB
(iv) CM = AB

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