Question

Show that the midpoint of the hypotenuse is equidistant from the vertices

Answer 1

Let P be the mid point of the hypo. of the right triangle ABC, right angled at B.

Draw a line parallel to BC from P meeting AB at D.

Join PB.

in triangles,PAD and PBD,

angle PDA= angle PDB (90 each due to conv of mid point theorem)

PD=PD(common)

AD=DB( as D is mid point of AB)

so triangles PAD and PBD are congruent by SAS rule.

PA=PB(C.P.C.T.)

but

PA=PC(given as P is mid point )

So,

PA=PC=PB