In geometry class, this property was quickly introduced: a/b=c/d=>(a+c)/(b+d)=a/b=c/d It usually avoids some boring quadratic equations, so it's useful but I don't really get it. Seems trivial but I can't prove. How to demonstrate it?

Leila Jennings 2022-07-14 Answered
Why a b = c d a + c b + d = a b = c d ?
In geometry class, this property was quickly introduced:
a b = c d a + c b + d = a b = c d
It usually avoids some boring quadratic equations, so it's useful but I don't really get it. Seems trivial but I can't prove.
How to demonstrate it?
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Answers (2)

slapadabassyc
Answered 2022-07-15 Author has 21 answers
a b = c d a + c b + d = a + a d b b + d = a b + a d b ( b + d ) = a b = c d

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Caylee Villegas
Answered 2022-07-16 Author has 2 answers
Assume that none of the unknowns is zero. Then, let
a b = c d = k
This implies,
a = k b , c = k d
a + c = k ( b + d )
a + c b + d = k

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