Question

几何好的,如图,AD//BC,∠A=∠C,BE、DF分别平分∠ABC和∠CDA,试说明BE//DF

Answer 1

∵AD//BC

∴∠A+∠ABC=180°

∠C+∠CDA=180°

∴∠A=∠C

∠ABC=∠CDA

∵BE、DF分别平分∠ABC和∠CDA

∴∠EBF=∠EDF=1/2∠ABC=1/2∠CDA

∵AD//BC

∴∠EDF=∠DFC

∴∠EBF=∠DFC

∴BE//DF