Question

如图所示,在△ABC中,∠ACB=90°,△CAD≌△CED,△CEF≌△BEF,△CEF≌△CAD.

Answer 1

(1)

因为△CAD≌△CED,所以∠1 = ∠2.

因为△CEF≌△CAD,所以∠2 = ∠3.

而∠ACB = 90°,所以∠1 = ∠2 = ∠3 = 90°÷3 = 30°.

因为△CEF≌△BEF,所以∠B = ∠3 = 30°.

(2)

因为△CEF≌△BEF,所以∠CFE = ∠BFE.

而∠CFE + ∠BFE = ∠CFB = 180°,所以∠BFE = 90°.

又∠BCA = 90°,所以EF∥AC.