Prove that the midpoint of hypotenuse of right angle triangle is equidistant from three vertices
Asked by sachin0706 | 22nd Mar, 2009, 06:50: PM
Expert 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 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
Answered by | 28th Nov, 2017, 02:51: PM
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