如图,梯形ABCD中,AD∥BC,点E在BC上,AE=BE,且AF⊥AB,连接EF. (1)若EF⊥AF,AF=4,AB=6,求 AE的长. (2)若点F是CD的中点,求证:CE=BE-AD.

问题描述:

如图,梯形ABCD中,AD∥BC,点E在BC上,AE=BE,且AF⊥AB,连接EF.

(1)若EF⊥AF,AF=4,AB=6,求 AE的长.
(2)若点F是CD的中点,求证:CE=BE-AD.

(1)作EM⊥AB,交AB于点M.∵AE=BE,EM⊥AB,∴AM=BM=12×6=3;∵EF⊥AF,∴∠AME=∠MAF=∠AFE=90°,∴四边形AMEF是矩形,∴EF=AM=3;在Rt△AFE中,AE=AF2+EF2=5;(2)延长AF、BC交于点N.∵AD∥EN,∴∠DAF=∠N...