Question

如图,已知ab//cd.∠1=∠b,∠2=∠d.求证be⊥ed.

Answer 1

AB//CD =>∠A+∠C=180° ----(1)

∠1=∠B =>∠A=180°-2∠1----(2)

∠2=∠D=>∠C=180°-2∠2----(3)

(2)+(3)=>∠A+∠C=360°-2(∠1+∠2)----(4)

(1)(4)=>180°=360°-2(∠1+∠2)=>∠1+∠2=90°

∴∠BED=180°-(∠1+∠2)=90°=>BE⊥ ED