Question

在RT三角形ABC中,角A=90,AD垂直于BC于D,求证：AB方=BD*BC

Answer 1

设BD=x,AD=h,BC=a,AC=b,AB=c,则DC=a-x

由勾股定理:

h^2+x^2=c^2

h^2+(a-x)^2=b^2

c^2+b^2=a^2

联立以上三式消去b,h得到:c^2=ax

即AB^2=BD*BC