如图,在△ABC中,∠ACB=90°,AC=BC,点P在AB上,AD⊥CP于点D,BE⊥CP于点E,BE=6cm.求CD的长.
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![如图,在△ABC中,∠ACB=90°,AC=BC,点P在AB上,AD⊥CP于点D,BE⊥CP于点E,BE=6cm.求CD的长.](/uploads/image/z/14234915-11-5.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E2%88%A0ACB%3D90%C2%B0%2CAC%3DBC%2C%E7%82%B9P%E5%9C%A8AB%E4%B8%8A%2CAD%E2%8A%A5CP%E4%BA%8E%E7%82%B9D%2CBE%E2%8A%A5CP%E4%BA%8E%E7%82%B9E%2CBE%3D6cm.%E6%B1%82CD%E7%9A%84%E9%95%BF.)
如图,在△ABC中,∠ACB=90°,AC=BC,点P在AB上,AD⊥CP于点D,BE⊥CP于点E,BE=6cm.求CD的长.
如图,在△ABC中,∠ACB=90°,AC=BC,点P在AB上,AD⊥CP于点D,BE⊥CP于点E,BE=6cm.求CD的长.
如图,在△ABC中,∠ACB=90°,AC=BC,点P在AB上,AD⊥CP于点D,BE⊥CP于点E,BE=6cm.求CD的长.
∵∠ACB=90°,AC=BC
∴∠CAB=∠CBA=45°
∵AD⊥CP,BE⊥CP,
∴∠CEB=∠ADC=90°
∴AD∥BE
∴∠DAP=∠EBP
∵∠BCE=180°-90°-∠CBA-∠EBP=45°-∠EBP
∠CAD=∠CAP-∠DAP=45°-∠DAP=45°-∠EBP=∠BCE
∴在△ACD和△CBE中,
∠CAD=∠BCE,∠ADC=∠CEB,AC=AB,
∴△ACD≌△CBE(AAS)
∴CD=BE=6cm