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数学
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如图,平行四边形ABCD中,∠BAD的平分线AE交BC的延长线于点E,交CD于点F,AB=5,BC=2,求CF的长.
人气:225 ℃ 时间:2020-03-20 02:18:02
解答
在▱ABCD中,
∵AB∥CD,
∴△EFC∽△EAB.
∴
CE
BE
=
CF
AB
.
∴
CE
BE
=
CF
5
.
又∵AD∥BC,AE平分∠BAD,
∴∠BAE=∠EAD=∠E.
∴BE=BA=5.
又∵BC=2,
∴CE=3.
∴
3
5
=
CF
5
.
∴CF=3.
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