如图,B是∠CAF内一点,点D在AC上,点E在AF上,且DC=EF,△BCD与△BEF的面积相等,求证：AB平分∠CAF,

Question

如图,B是∠CAF内一点,点D在AC上,点E在AF上,且DC=EF,△BCD与△BEF的面积相等,求证：AB平分∠CAF,

Answer 1

证明：过点B作BM⊥AC于M,BN⊥AF于N
∵BM⊥AC,BN⊥AF
∴S△BCD＝CD×BM/2, S△BEF＝EF×BN/2
∵S△BCD＝S△BEF
∴CD×BM/2＝EF×BN/2
∵CD＝EF
∴BM＝BN
∴AB平分∠CAF