Question

已知,如图所示∠abc为直角三角形纸片,∠c＝90°,ac≤bc,将纸片沿ef折叠,使a点落在bc上d,若△dce与

Answer 1

∵∠C=90°CE=CD,∴∠CDE=45°,∠A=90°-∠B.

∵△EAF≌△EDF, ∴∠EDF=∠A=90°-∠B.

∵△FBD是等腰三角形,∴∠BDF=∠BFD,∴∠BFD=1/2(90°-∠B)=45°-1/2∠B,

∵∠CDF=∠BFD+∠B,∠CDE+∠EDF=∠BFD+∠B,

∴45°+90°-∠B=45°-1/2∠B+∠B

3/2∠B=45°

∠B=30°