Question

如图,△ABC是等腰直角三角形,BC是斜边,点D是三角形内一点,且AD=根号2,BD=2根号3,CD=4,试求∠ADC

Answer 1

把△ABD逆时针旋转90度,得一新△ACE,则△ABD≌△ACE,

连结DE,△ADE是等腰RT△,

〈ADE=〈AED=45°,

DE=√2AD=2,

CE=BD=2√3,

CD=4,

DE^2+CE^2=CD^2=16,

∴△DEC是RT△,