Question

等腰梯形一条对角线与一腰垂直,上底=腰长=1,下底长为?

Answer 1

设梯形ABCD,AD∥BC,AD=AB=CD=1,BD⊥CD.求BC.

∵AD=AB

∴∠ADB=∠ABD

∵AD∥BC

∴∠ADB=∠DBC

∴∠ABD=∠DBC

∴∠ABC=2∠DBC

∵AD∥BC AB=CD

∴∠C=∠ABC=2∠DBC

∵BD⊥CD

∴∠BDC=90°

∴∠C+∠DBC=90°

∴∠DBC=30°

∵DC=1

∴BC=2CD=2