\(\frac{a}{b}=\frac{c}{d}=\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2=\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a^2+c^2}{b^2+d^2}\)(T/c dãy tỷ số = nhau)(1)
\(\frac{a}{b}=\frac{c}{d}=\frac{a+b}{c+d}\Rightarrow\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2=\left(\frac{a+c}{b+d}\right)^2\)
\(\Rightarrow\frac{a}{b}=\frac{c}{d}=\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{\left(a+c\right)^2}{\left(b+d\right)^2}\)(2)
Từ )1) và (2) =>\(\frac{a^2+c^2}{b^2+d^2}=\frac{\left(a+c\right)^2}{\left(b+d\right)^2}\)