10. Prove that the mid-point of the hypotenuse of a right002triangle i

1.	10. Prove that the mid-point of the hypotenuse of a right002triangle is equidistant from its vertices.
Answer» 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 toconv 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

10. Prove that the mid-point of the hypotenuse of a right002triangle is equidistant from its vertices.

Answer»

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 toconv 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