已知如图在三角形ABC中AD是三角形ABC的角平分线E是AB上一点,AE=AC.EF平行BC交AC与点F,过点C分别作E

你题目抄错啦!是CG = CH,不是CD = CH!
CDH是直角三角形,CD是直角对边,因此 CD > CH!
(证明 CG = CH)
∵ AD为角平分线,∴ ∠BAD = ∠CAD
∵ ∠BAD = ∠CAD,AE = AC,AD共线,∴ △AED ≌ △ACD (SAS) => ED = CD
∵ △CDE,ED = CD,∴∠CED = ∠ECD
∵ EF∥BC,∴ ∠CEG = ∠ECD = ∠CED
∵ △CHE & △CGE中,∠CEG = ∠CED,∠CHE = ∠CGE = 90︒,CE共线,∴ CG = CH