已知:如图,在三角形ABC中,AD垂直于BC,垂足为点D,AD^2=BD*DC.求证:三角形ABC是直角三角形.今晚之前给我,最好8:15之前交给我
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![已知:如图,在三角形ABC中,AD垂直于BC,垂足为点D,AD^2=BD*DC.求证:三角形ABC是直角三角形.今晚之前给我,最好8:15之前交给我](/uploads/image/z/746105-41-5.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%2CAD%E5%9E%82%E7%9B%B4%E4%BA%8EBC%2C%E5%9E%82%E8%B6%B3%E4%B8%BA%E7%82%B9D%2CAD%5E2%3DBD%2ADC.%E6%B1%82%E8%AF%81%EF%BC%9A%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E6%98%AF%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2.%E4%BB%8A%E6%99%9A%E4%B9%8B%E5%89%8D%E7%BB%99%E6%88%91%EF%BC%8C%E6%9C%80%E5%A5%BD8%EF%BC%9A15%E4%B9%8B%E5%89%8D%E4%BA%A4%E7%BB%99%E6%88%91)
已知:如图,在三角形ABC中,AD垂直于BC,垂足为点D,AD^2=BD*DC.求证:三角形ABC是直角三角形.今晚之前给我,最好8:15之前交给我
已知:如图,在三角形ABC中,AD垂直于BC,垂足为点D,AD^2=BD*DC.求证:三角形ABC是直角三角形.
今晚之前给我,最好8:15之前交给我
已知:如图,在三角形ABC中,AD垂直于BC,垂足为点D,AD^2=BD*DC.求证:三角形ABC是直角三角形.今晚之前给我,最好8:15之前交给我
∵AD²=BD*DC,∴BD/AD=AD/DC
又∵ΔADB,ΔCDA为直角三角形
∴ΔADB∽ΔCDA,(一角相等,夹这个角的两边对应成比例)
∴∠BAD=∠C,∠B=∠CAD
∴∠A=∠BAD+∠CAD=180º/2=90º
∴ΔABC是直角三角形
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