Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

Explanation

Let `P`be the mid point of the hypotenuse of the right `/_\ABC` right angled at `B`
Draw a line parallel to `BC \from\ P` meeting `B \at\ O`
Join `PB`
In `/_\ PAD and /_\ PBD`
`/_PDA=/_PDB90^0`(each due to conv of mid point theorem)
`PD=PD`(common)
`AD=DB` (As D is mid point of AB)
So `/_\ PAD~=/_\ PBD` (SAS rule)
`PA=PB`(C.P.C.T.)
`PA=PC`(Given P is the mid point)
`PA=PC=PC`