已知:如图,在△ABC中,点E在边BC上,将ABE沿直线AE折叠
1个回答

∵将△ABE沿直线AE折叠,点B恰好落在边AC上的点D处,

∴△ABE≌△ADE,

∴∠B=∠ADE,AB=AD=5,

∵∠FCA=∠B,

∴∠FCA=∠ADE,

∴DE∥CF,

∴△ADE∽△ACF,

∴DECF=ADAC=59,

∴BECF=59;

∵∠FCA=2∠ACB,

∴∠ACE=∠FCE.

∵DE∥CF,

∴∠DEC=∠FCE,

∴∠ACE=∠DEC,

∴DE=DC=AC-AD=9-5=4,

∵△ABE≌△ADE,

∴BE=DE=4

∵BE:CF=5:9

∴CF=7.2