In a 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) ∆ AMC ~= ∆ BMD
ii) angle DBC is a right angle
iii) CM = ½ AB .

class 9 ​