Complete the paragraph proof.
You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, StartFraction c Over a EndFraction = . This can be rewritten as = a2. Using ratios from the large and small triangles, = StartFraction b Over e EndFraction. This can be rewritten as b2 = ec. By substitution, a2 + b2 =. You can then factor as a2 + b2 = c(f + e). From the large triangle, you know (f + e) =. So, a2 + b2 = c2 by using substitution.