在梯形ABCD中,AB∥CD,若DB,AC交于点O,且△DCO的面积与△DCB的面积比为1:3,则△CDO与△ABO的面积比等于(  ) A.1:9 B.1:7 C.1:4 D.1:5

问题描述:

在梯形ABCD中,AB∥CD,若DB,AC交于点O,且△DCO的面积与△DCB的面积比为1:3,则△CDO与△ABO的面积比等于(  )
A. 1:9
B. 1:7
C. 1:4
D. 1:5

∵AB∥CD,
∴△DOC∽△BOA,

S△DOC
S△BOA
=(
DO
BO
)2
S△DCO
S△DBC
=
1
3

DO
DB
=
1
3

DO
BO
=
1
2

S△DOC
S△BOA
=(
1
2
)
2
=
1
4

故选C.