Question

八年级数学解答题、证明题!请速度解答，要有详细的步骤。谢谢!

1.图图" class="ikqb_img_alink">已知等边三角形ABC∠ABC平线与∠ACB平线相交于O点OD平行ABOE平行AC试说明:(1)△ODE等边三角形(2)BD=DE=EC 2.图图" class="ikqb_img_alink">△ABCBD平∠ABCCD平∠ACB外角点D作DE平行BC交AB于EAC于F试问EF与BE、CF关系何 3.图图" class="ikqb_img_alink">,△ABC,∠B=2∠C,AD∠A平线,求证:AC=AB+BD. 4.已知:图图" class="ikqb_img_alink">△ABCAD平行BC∠B=∠C求证:AD平∠EAC

Answer 1

2.
由DE∥BC∠EDB=∠DBC=∠ABD所BE=ED
仍由DE∥BC∠CDE=∠DCH=∠ACD所CF=FD
即:BE=ED=EF+FD=EF+CF
3.
AC取点E使AE=AB连接DE
易证△ABD≌△AED则BD=ED且∠B=∠AED=∠C+∠CDE
∠B=2∠C所∠C=∠CDE则DE=EC
于AC=AE+EC=AB+BD
4.
∵
AD∥BC∴
∠EAD=∠B∠DAC=∠C
∵∠B=∠C∴
∠EAD=∠DAC
即AD平∠CAE