Question

点D、E分别是等边△ABC的边AC、BC上的点,AD=CE,BD、AE交于点P,BQ⊥AE于Q,探究PQ与PB之间的数量

Answer 1

BP=2PQ

∵ABC为正三角形

∴AB=AC ∠BAC=∠ACB

∵AD=CE

∴△ABD≌△ACE

∠ABD=∠CAE

∵∠APD=∠ABP+∠BAP=∠CAE+∠BAP=60°

∴∠BPQ=∠APD=60°

∵BQ⊥AE

∴BP=2PQ