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已知:如图,在直角三角形ABC中,∠BAC=90o,AB=AC,∠DAE=45o求证BC^2=2BE·CD

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已知:如图,在直角三角形ABC中,∠BAC=90o,AB=AC,∠DAE=45o求证BC^2=2BE·CD
已知:如图,在直角三角形ABC中,∠BAC=90o,AB=AC,∠DAE=45o求证BC^2=2BE·CD
证明:AB=AC,∠BAC=90°,则:∠B=∠C=45°.
∠AEB=∠C+∠CAE=45°+∠CAE;
∠DAC=∠DAE+∠CAE=45°+∠CAE.
故∠AEB=∠DAC;
则⊿BEA∽⊿CAD,BE/CA=AB=CD,AB*CA=BE*CD,AB^2=BE*CD.
故:BC^2=AB^2+AC^2=2AB^2=2BE*CD.