Question

如图,已知点D为△ABC内一点,求证:∠BDC>∠A

Answer 1

因为∠A+∠ABC+∠ACB=180°

∠BDC+∠CBD+∠BCD=180°

所以∠A=180°-(∠ABC+∠ACB)

∠BDC=180°-(∠CBD+∠BCD)

又因为∠CBD所以∠CBD+∠BCD于是180°-(∠CBD+∠BCD)>180°-(∠ABC+∠ACB)

即∠BDC＞∠A