Question

如图，已知∠1=∠2，∠3=∠4.求证AC=AD.

(用∵，∴形式回答,运用AAS)

Answer 1

∵∠3=∠4、∠1=∠2
∴∠BAC=∠3-∠1=∠4-∠2=∠BAD
又∵AB=AB
∴ΔABC≌ΔABD(ASA)
∴AC=AD

∵∠3=∠4
∠ACB=180°-∠3=180°-∠4=∠ADB
又∴∠1=∠2、AB=AB
∴ΔABC≌ΔABD(AAS)
∴AC=AD

Answer 2

证明∵∠CAB=∠3-∠1
∠DAB=∠4-∠2
又∵∠1=∠2，∠3=∠4
∴∠CAB=∠DAB
∴在ΔCAB和ΔDAB中
∠CAB=∠DAB
AB=AB
∠1=∠2
∴ΔCAB和ΔDAB全等
∴AC=AD

Answer 3

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