Question

初三几何体在△APC中,AP=PC,∠DBF=∠C.求证;AB乘BC=AD乘CF(点D在AP上,F在PC上,B在AC上)

Answer 1

证明：∵AP=PC,∠DBF=∠C,∠DBF=∠C∴∠A=∠DBF=∠C

∵∠A+∠CBF+∠ABD=180°；∠C+∠CBF+∠CFB=180°

∴∠ABD=∠CFB

∵∠ABD=∠CFB,∠A=∠C

∴△ABD∽△CFB

∴AB:CF=AD:BC

∴AB乘BC=AD乘CF