Given: right triangle abc with altitude prove: a2 + b2 = c2 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, = . this can be rewritten as = a2. using ratios from the large and small triangles, = . 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.