Question

请教数学相似三角形的题在矩形ABCD中,AB=6cm,BC=8cm,将矩形ABCD折叠,使B和D重合,BD与EF相交于点

Answer 1

根据对称性可知：折痕EF是对角线BD的垂直平分线,

可得：点O为BD的中点,

又AD‖BC,可得：点O为EF的中点.

AD = BC = 8cm ,

BD = √(AD²+AB²) = 10cm ,

可得：OD = 5cm .

因为,AB∶AD = tan∠ADB = OE∶OD ,

所以,OE = AB·OD/AD = 3.75cm ,

可得：EF = 2·OE = 7.5cm .