AD平分角BAC,AD与BC交于D点,CE⊥AD于M,交AB于E,EF‖BC交AC于F.求证：EC平分∠DEF

AD平分角BAC,AD与BC交于D点,CE⊥AD于M,交AB于E,EF‖BC交AC于F.求证：EC平分∠DEF
AD平分角BAC,AD与BC交于D点,CE⊥AD于M,交AB于E,EF‖BC交AC于F.求证：EC平分∠DEF

AD平分角BAC,AD与BC交于D点,CE⊥AD于M,交AB于E,EF‖BC交AC于F.求证：EC平分∠DEF
∵EF‖BC ∴∠3=∠4 ,
AM平分∠A ,EC⊥AM ,∴AM是角的垂直平分线 ,∴DE=DC,∴∠5=∠3
∴∠5=∠4 
所以EC平分∠DEF