Question

如图,已知在Rt△ABC中,AB=AC,CD是∠ACB的平分线,交AB于D,DE⊥BC于E,若BC=20cm,求△BDE

Answer 1

因为,在△CDA和△CDE中,∠CAD = 90° = ∠CED ,∠ACD = ∠ECD ,CD为公共边,

所以,△CDA ≌ △CDE ,

可得：DA = DE ,AC = EC ；

△BDE的周长 = BE+BD+DE = BE+BD+DA = BE+AB = BE+AC = BE+EC = BC = 20cm .