Question

在△abc中，ab=ac,ad是∠bac的平分线，e为ad延长线上一点，cf平行于be且交ad于f连接bf,ce。

证明四边形becf是菱形。

Answer 1

证明：如图：∵ AB=AC ,AD为∠ BAC的平分线

            ∴ AD⊥BC  BD=DC

                     又∵CF‖BE

                      ∴ ∠1=∠2

                  在Rt△BDE和Rt△CDF中

            ∵∠1=∠2 

                           BD=CD

                         ∠BDE=∠CDF=90°

                    ∴Rt△BDE ≌ Rt△CDF（角、边、角）               

                  ∴BE=CF

                            又∵BE‖CF

                           ∴四边形BECF为平行四边形

                又∵ FE⊥BC

                            ∴四边形BECF为菱形

                       《证毕》！