几何第二册第146页B组第二题:一组对角相等一组对边相等的四边形是平行四边形吗?李俊杰同学认为是对的,他的证明如下: 已知如图1,四边形ABCD中,∠B=∠D,AB=CD, 求证四边形ABCD是平行四边形. 证明分别过A、C作AE⊥BC于E,CF⊥AD于F→∠AEB=∠CFD=90°,∠B=∠D,AB=CD,则Rt△ABE≌Rt△CDF→①BE=DF,②AE=CF.连结 AC.在Rt△ACE与 Rt△CAF中,∠AEC=∠CFD=90°,AC=CA,已证AE= The second volume of the second volume of the second book on page 146 of the second volume: a group of diagonal equals and a group of quadrilaterals with equal sides are parallelograms? Junjay Li thinks it is right. His proof is as follows: Known as Figure 1, Quadrilateral ABCD In the middle, ∠B=∠D, AB=CD, verify that the quadrilateral ABCD is a parallelogram. Prove that AE and C are respectively AE⊥BC in E, CF⊥AD in F→∠AEB=∠CFD=90°,∠B= ∠ D, AB = CD, then Rt △ ABE ≌ Rt △ CDF → 1BE = DF, 2AE = CF. Link AC. In Rt △ ACE and Rt △ CAF, ∠ AEC = ∠ CFD = 90 °, AC = CA, AE certified