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Answer :

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]

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