Question

如图,在直角三角形ABC中,角BAC为直角,AD垂直于BC于点D.求证（1）AB^2=BD*BC,AC^2=CD*CB;

Answer 1

⑴在RTΔCAB与RTΔCDA中,

∠C=∠C,

∴RTΔCAB∽RTΔCDA,

∴AC/CD=BC/AC,

∴AC^2=CD*BC.

同理：AB^2=BD*BC.

⑵∵∠BAC=90°,∠B+∠C=90°,

∵AD⊥BC,∴∠CAD+∠C=90°,

∴∠CAD=∠B,

∴RTΔADC∽RTΔBDA,

∴AD/CD=BD/AD,

∴AD^2=BD*CD.