Question

△ABC为等边三角形,∠BDC为120°.求证BD+CD=AD

Answer 1

延长BD到E,并使DE=DC,∠CDE=180°-∠BDC=

180°-120°=60°

△DCE为等边△→ DC=EC------边

∠DCE =60°=∠ACB→ ∠ACD =∠BCE----角

△ABC为等边△→AC=BC----------------边

边角边→△ACD≌△BCEAD=BE=BD+DE=BD+DC