Given that:

Prove that:

((distance AB) ⋅ (distance AB)) + ((distance AC) ⋅ (distance AC)) = ((distance BC) ⋅ (distance BX)) + ((distance BC) ⋅ (distance CX))

The following properties may be helpful:

if a / b = c / d, then a ⋅ d = b ⋅ c
if a / b = c / d, then a ⋅ d = b ⋅ c
if x ⋅ (distance AB) = (distance CD) ⋅ y, then x ⋅ (distance BA) = (distance DC) ⋅ y
if x ⋅ (distance AB) = z, then x ⋅ (distance BA) = z
if the following are true:
- a = b
- c = d
then a + c = b + d

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

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