Question

如图,在△ABC中,BA=BC,∠ABC=45°,AH是BC边上的高，E是AH上的一点，EH=CH，连接EC，求证EA=EC

图片

Answer 1

∠ABC=45°
∠AHB=90°
=>∠BAH=45°
BA=BC
∠ABC=45°
=>∠BAC=∠BCA=(180°-45°)/2=67.5°
=>∠HAC=∠BAC-∠BAH=22.5°

∠EHA=90°
EH=HC
=>∠HCE=45°
=>∠ECA=∠BCA-∠HCE=22.5°
∠ECA=∠BCA-∠HCE=22.5°

∠HAC=∠BAC-∠BAH=22.5°
=>EA=EC