Question

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 $CM=\frac{1}{2}AB$

Answer 1

$AM=BM=\frac{1}{2}AB$

$\Rightarrow \angle =90°$

$DM=CM$

$△DBM$ and $△BCM$

$\Rightarrow BM=BM$ ( common )

$DM=CM$ ( given )

$\angle DMB\cong △BCM$

$\therefore BM=CM=\frac{1}{2}AB$

Hence, solved.