Question

如图,在△ABC中,∠C=90°,∠A=30°,求证AB=2BC

Answer 1

证明：过C点做 ∠ACD = 30° ,交AB于D,

因为 ∠A = ∠ACD = 30° ,

所以 AD = CD

又 ∠DCB = ∠ACB - ∠ACD = 90° - 30° = 60°

而 ∠B = ∠ACB - ∠A = 90° - 30° = 60°

所以 ∠DCB = ∠B = ∠CDB = 60°

所以 CD = BC = BD

所以 AD = CD = BD = BC

所以 AB = AD + BD = BC +BC =2BC