You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, Start Fraction c Over a Infraction = . This can be rewritten as = a2. Using ratios from the large and small triangles, = Start Fraction b Over e Infraction. 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.