Prove that line joining the mid point of hypotenuse of right angled tr

1.	Prove that line joining the mid point of hypotenuse of right angled triangle to opposite vertex is half the hypotenuse.
Answer» Given : In right angled ΔABC ∠ABC = 90° and point M is mid point of hypotenuse AC To Prove : BM = AM = CM Construction : Taking AC as a diameter draw a circle which passes through B. Proof : Hypotenuse AC diameter circle, of right ΔABC, AC is M is mid point of AC so M will be center of circle Thus, AM = MC …(i) [M is mid point] BM = MC ….(ii) [Radius of circle] From equations (i) and (ii) BM = AM = MC = \(\frac { 1 }{ 2 }\)AC,

Prove that line joining the mid point of hypotenuse of right angled triangle to opposite vertex is half the hypotenuse.

Answer»

Given : In right angled ΔABC

∠ABC = 90° and point M is mid point of hypotenuse AC

To Prove : BM = AM = CM

Construction : Taking AC as a diameter draw a circle which passes through B.

Proof : Hypotenuse AC diameter circle, of right ΔABC, AC is

M is mid point of AC so M will be center of circle

Thus, AM = MC …(i) [M is mid point]

BM = MC ….(ii) [Radius of circle]

From equations (i) and (ii)

BM = AM = MC = \(\frac { 1 }{ 2 }\)AC,

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Prove that line joining the mid point of hypotenuse of right angled triangle to opposite vertex is half the hypotenuse.

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