16. Exercise Problems VIII

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) \(∆ AMC ≅ ∆ BMD\)

 

(ii) \(∠DBC\) is a right angle.

 

(iii) \(∆ DBC ≅ ∆ ACB\)

 

(iv) \(CM =  \frac{1}{2} AB\)