`a,a/c=b/d`
`⇒a/c-1=b/d-1`
`⇒a/c-c/c=b/d-d/d`
`⇒{a-c}/c={b-d}/d` `(đpcm)`
`b,a/c=b/d`
`⇒a/b=c/d`
`⇒a/b=c/d={a+c}/{b+d}={a-c}/{b-d}` `(DTSBN)`
`⇒{a+c}/{b+d}={a-c}/{b-d}` `(đpcm)`
`c,a/c=b/d`
`⇒a/b=c/d`
`⇒{3a}/{3b}={4c}/{4d}`
`⇒{3a}/{3b}={4c}/{4d}={3a+4c}/{3b+4d}={3a-4c}/{3b-4d}` `(DTSBN)`
`⇒{3a+4c}/{3b+4d}={3a-4c}/{3b-4d}`
`⇒{3a+4c}/{3a-4c}={3b+4d}/{3b-4d}` `(đpcm)`
`d,a/c=b/d`
`⇒a/c=b/d={a+b}/{c+d} (DTSBN)`
`⇒(a/c)^2=(b/d)^2=({a+b}/{c+d})^2`
`⇒a^2/c^2=b^2/d^2={(a+b)^2}/{(c+d)^2}`
`Vì` `a^2/c^2=b^2/d^2={a^2+b^2}/{c^2+d^2}` `(DTSBN)`
`⇒{a^2+b^2}/{c^2+d^2}={(a+b)^2}/{(c+d)^2}` `(đpcm)`
