Question

I'm having trouble answers these questions b-h. I've already answered a. I can provide a photo of a if needed. this assignment is over the pythagorean theorem.

Answer 1

With the triangles given:

Then, the proportion for first triangle and second triangle would be:

`\begin{gathered} (b)/(c)=(d)/(b) \\ \text{Cross multiplication:} \\ b^2=d\cdot c \end{gathered}`

Proportin for first triangle and third triangle:

`\begin{gathered} (c)/(a)=(a)/(e) \\ Cross\text{ multiplication} \\ c\cdot e=a^2 \end{gathered}`

f. The equations would be:

`\begin{gathered} b^2=d\cdot c \\ a^2=c\cdot e \\ a^2+b^2=(d\cdot c)+(c\cdot e) \end{gathered}`

g. Then, factor out a common factor:

`a^2+b^2=c(d+e)`

h. As a final step, replace the expression inside the parenthesis with one variable and then simplify:

`\begin{gathered} a^2+b^2=c(c) \\ a^2+b^2=c^2 \end{gathered}`