如图所示,四边形ABCD是矩形,把△ACD沿AC折叠到△ACD′,AD′与BC交于点E,若AD=4,DC=3,求BE的长.

问题描述:

如图所示,四边形ABCD是矩形,把△ACD沿AC折叠到△ACD′,AD′与BC交于点E,若AD=4,DC=3,求BE的长.

∵四边形ABCD为矩形,∴AB=DC=3,BC=AD=4,AD∥BC,∠B=90°,∵△ACD沿AC折叠到△ACD′,AD′与BC交于点E,∴∠DAC=∠D′AC,∵AD∥BC,∴∠DAC=∠ACB,∴∠D′AC=∠ACB,∴AE=EC,设BE=x,则EC=4-x,AE=4-x,在Rt...