Question

如图,把矩形ABCD沿EF对折,点A与点C重合,若AC=6cm,BC=8cm,求证四边形AFCE为菱形；求EF长

Answer 1

①由对折可知,EF⊥AC,且AO＝OC,又AD∥BC,∴∠DAC＝∠BCA,∠AEO＝∠CFO,AO＝OC,∴⊿AEO≌⊿CFO,∴EO＝FO,又AO＝OC,EF⊥AC,∴四边形AFCE为菱形.②由AB＝6,BC＝8,得AC＝10,CO＝5,又由⊿CFO∽⊿CAB,得FO／5＝6／8,∴FO＝15／4,∴EF＝2FO＝15／2.