已知:如图,△ABC中,AB=AC,∠ABC、∠ACB的平分线交于点E,直线AE交BC于D.求证:AD⊥BC证明:∵AB=AC(已知),∴∠ABC=∠ACB(______)∵BE平分∠ABC(已知),CE平分∠ACB(已知),∴∠EBD=12__-数学
题文
已知:如图,△ABC中,AB=AC,∠ABC、∠ACB的平分线交于点E,直线AE交BC于D. 求证:AD⊥BC 证明:∵AB=AC (已知),∴∠ABC=∠ACB (______ ) ∵BE平分∠ABC (已知),CE平分∠ACB (已知), ∴∠EBD=
∴∠EBD=∠ECD ( 等量代换 ), ∴BE=CE (______ ), 在△ABE和△ACE中, ∵
∴△ABE≌△ACE (______), ∴∠BAE=∠CAE (全等三角形对应角相等), ∵AB=AC (已知), ∴AD⊥BC (______). |