如圖所示,在菱形ABCD中,∠ABC=60°,DE‖AC交BC的延長線於點E.求證:DE=12BE.

如圖所示,在菱形ABCD中,∠ABC=60°,DE‖AC交BC的延長線於點E.求證:DE=12BE.

證明:法一:如右圖,連接BD,∵四邊形ABCD是菱形,∠ABC=60°,∴BD⊥AC,∠DBC=30°,∵DE‖AC,∴DE⊥BD,即∠BDE=90°,∴DE=12BE.法二:∵四邊形ABCD是菱形,∠ABC=60°,∴AD‖BC,AC=AD,∵AC‖DE,∴四邊形…