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\(ABC\) is a triangle right angled at \(C\). A line through the mid-point \(M\) of hypotenuse \(AB\) and parallel to \(BC\) intersects \(AC\) at \(D\).
Show that
(i) \(D\) is the mid-point of \(AC\)
(ii) \(MD ⊥ AC\)
(iii) \(CM = MA = \frac{1}{2}AB\)
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Important!
The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.
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