初二数学：平行线分对应线段成比例

题目

初二数学：平行线分对应线段成比例
1.三角形ABC的三边是a,b,c,三边上的高分别是ha,hb,hc,且ha:hb:hc:=5:2:c,求a:b:c
2.AB,CD是梯形ABCD的底,对角线AC,BD的交点是O,AB=12,CD=4,BD=15,求OB,OD.

答案

1. a × ha = b × hb = c × hca : b = hb : ha = 2 : 5 = 2c : 5cb : c = hc : hb = c : 2 = 5c : 10a : b : c = 2c : 5c : 102.OB : OD = AB : CD = 12 : 4 = 3 : 1OB ＋ OD = BD = 15OB = 45/4 OD = 15/4