如图矩形ABCD中,延长CB到E,使CE=AC,F是AE中点.求证:BF⊥DF.

问题描述:

如图矩形ABCD中,延长CB到E,使CE=AC,F是AE中点.求证:BF⊥DF.

证明:延长BF,交DA的延长线于点M,连接BD,∵四边形ABCD是矩形,∴MD∥BC,∴∠AMF=∠EBF,∠E=∠MAF,又FA=FE,∴△AFM≌△EFB,∴AM=BE,FB=FM,∵在矩形ABCD中,∴AC=BD,AD=BC,∴BC+BE=AD+AM,即CE=MD,∵CE=A...