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

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

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

如图,已知AC=BC,AC⊥BC,DC⊥EC,且∠CAD=∠CBE.求证:CD=CE.
∵AC⊥BC、DC⊥EC,∴∠ACD=∠ACB-∠BCD=90°-∠BCD=∠DCE-∠BCD=∠BCE.
由∠ACD=∠BCE、∠CAD=∠CBE、AC=BC,得:△ACD≌△BCE,∴CD=CE.