Question

如图所示,已知AE=AC,EF‖BC,EC平分∠DEF,求证：AD⊥EC

Answer 1

EF‖BC,可得∠CEF = ∠BCE

EC为角平分线,可得∠CEF = ∠CED

所以∠BCE = ∠CED,即△DCE是等腰三角形,DE = DC

又因为AE = AC,AD为公共边,所以△ADE ≌ △ADC,则∠ADE = ∠ADC,即DA为∠CDE的角平分线

等腰三角形,顶角角平分线就是底边上的高,所以AD⊥EC