Question

In the following diagram, triangle ABC is right-angled at triangle. L and M are the mid-points of side AC and AB respectively.
Prove that: BL^2 + CM^2 = 5ML^2.​

Answer 1

given = CL =AL, AM= BM

SOLUTION

LM^2= AL^2+ AM^2

LB^2=AL^2+ AB^2

CM^2=AC^2+AM^2

LM^2=AL^2+AM^2

adding eq. 2 and 3

LB^2+CM^2 = (AL^2+2AM^2)+(AM^2+ 2AL^2)

LB^2+CM^2= 3(AL^2+AM^2)

HENCE PROVED

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