Question

已知：如图,在Rt△ABC中,∠ACB=90°,AC=BC,点D是BC的中点,CE⊥AD,垂足为点E,BF//AC交CE

Answer 1

∵ AC = BC,D是BC的中点.

∴ AC = 2CD.

∵ ∠ACB = 90°,BF∥AC.

∴ ∠CBF = 90°.

∵ CE⊥AD

∴ ∠CED = 90°.

在△ACD与△CED中,∠CDA = ∠CDE,∠ACD = ∠CED,所以△ACD ∽ △CED.

∴ ∠ECD = ∠EAD.

在△ACD与△CBF中,AC = BC,∠CAD = ∠ECD = ∠BCF,∠ACD = ∠CBF,所以△ACD≌△CBF.

∴ CD = BF = (1/2)AC

∴ AC = 2BF