如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD

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如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD如图所示,已知梯形A

如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD
如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD

如图所示,已知梯形ABCD中,AD//BC,角ACD=角B,求证AB2/CD2=BC/AD
证明:
∵AD∥BC
∴∠DAC=∠BCA
又∵∠B=∠ACD
∴△DAC∽△ACB
∴AD:AC=DC:AB=AC:BC
∴AD:BC=AC^2:BC^2=CD^2:AB^2
即为 AB2/CD2=BC/AD

证明:
∵AD∥BC
∴∠DAC=∠BCA
又∵∠B=∠ACD
∴△DAC∽△ACB
∴AD:AC=DC:AB=AC:BC
∴AD:BC=AC^2:BC^2=CD^2:AB^2