In right triangle \( \mathrm{ABC} \), right angled at \( \mathrm{C}, \mathrm{M} \) is the mid-po...

In right triangle \( \mathrm{ABC} \), right angled at \( \mathrm{C}, \mathrm{M} \) is the mid-point of hypotenuse AB. C is joined to \( \mathrm{M} \) and produced to a point \( \mathrm{D} \) such that \( \mathrm{DM}= \) CM. Point \( \mathrm{D} \) is joined to point \( \mathrm{B} \) (see Fig. Show that:
(i) \( \triangle \mathrm{AMC} \cong \triangle \mathrm{BMD} \)
(ii) \( \angle \mathrm{DBC} \) is a right angle. C
(iii) \( \triangle \mathrm{DBC} \cong \triangle \mathrm{ACB} \)
(iv) \( \mathrm{CM}=\frac{1}{2} \mathrm{AB} \)