With the triangles given:
Then, the proportion for first triangle and second triangle would be:
[tex]\begin{gathered} \frac{b}{c}=\frac{d}{b} \\ \text{Cross multiplication:} \\ b^2=d\cdot c \end{gathered}[/tex]
Proportin for first triangle and third triangle:
[tex]\begin{gathered} \frac{c}{a}=\frac{a}{e} \\ Cross\text{ multiplication} \\ c\cdot e=a^2 \end{gathered}[/tex]
f. The equations would be:
[tex]\begin{gathered} b^2=d\cdot c \\ a^2=c\cdot e \\ a^2+b^2=(d\cdot c)+(c\cdot e) \end{gathered}[/tex]
g. Then, factor out a common factor:
[tex]a^2+b^2=c(d+e)[/tex]
h. As a final step, replace the expression inside the parenthesis with one variable and then simplify:
[tex]\begin{gathered} a^2+b^2=c(c) \\ a^2+b^2=c^2 \end{gathered}[/tex]
