作直角梯形ABCD,AB∥CD,∠B=∠C=90°,使BC=AB＋CD,在BC上取BE=CD=a,CE=AB=b,连接AE、DE,且AE=DE=c,∴△ABE≌△ECD,∴由面积关系得：½ab×2＋½c²=½﹙a＋b﹚×﹙a＋b﹚,化简得：a²＋b²=...