ABC is a triangle, right-angled at B. M is a point on BC. Hence,
$A M^{2} + B C^{2} = A D^{2} + B M^{2}$
State true or false.

True

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False

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Solution

The correct option is B False
Given, $∠ A B C = 90$ , M is a point of BC
In $△ A B M$ ,
$A B^{2} + B M^{2} = A M^{2}$ (Pythagoras theorem)
$A B^{2} = A M^{2} - B M^{2}$ (I)
In $△ A B C$ ,
$A B^{2} + B C^{2} = A C^{2}$ (Pythagoras Theorem)
$A B^{2} = A C^{2} - B C^{2}$ (II)
Equating I and II,
$A M^{2} - B M^{2} = A C^{2} - B C^{2}$
thus, $A M^{2} + B C^{2} = A C^{2} + B M^{2}$

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ABC is a triangle, right-angled at B. M is a point on BC. Hence,AM2+BC2=AD2+BM2State true or false.

The correct option is B FalseGiven, ∠ABC=90, M is a point of BCIn △ABM, AB2+BM2=AM2 (Pythagoras theorem)AB2=AM2−BM2 (I)In △ABC,AB2+BC2=AC2 (Pythagoras Theorem)AB2=AC2−BC2 (II)Equating I and II,AM2−BM2=AC2−BC2thus, AM2+BC2=AC2+BM2

ABC is a triangle, right-angled at B. M is a point on BC. Hence,
$A M^{2} + B C^{2} = A D^{2} + B M^{2}$
State true or false.