Question

如图,已知AC=BC,AC⊥BC,DC⊥EC,且∠CAD=∠CBE.求证：CD=CE.

Answer 1

∵AC⊥BC、DC⊥EC,∴∠ACD＝∠ACB－∠BCD＝90°－∠BCD＝∠DCE－∠BCD＝∠BCE.

由∠ACD＝∠BCE、∠CAD＝∠CBE、AC＝BC,得：△ACD≌△BCE,∴CD＝CE.