fie trapezul ABCD, AB||CD AB < CD si AA' si BB' inaltimi
B - b = A'D + B'C
AD² = A'A² + A'D²
BC² = B'B² + B'C²
AD² - BC² = A'D² - B'C²
(AD + BC)(AD - BC) = (A'D + B'C)(A'D - B'C) = (B - b)(A'D - B'C)
(AD - BC) = (B-b)(A'D - B'C)/(AD+BC)
(A'D - B'C)/(AD + BC) < 1 ⇒
⇒ AD - BC < B - b CD - AB > AD - BC
