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2009年山西省中考数学试题(含答案及详细解析) 

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由(2)知四边形BC1DA是菱形, ∴AD?AB?2, ∴ED?AD?AE?2?23 ························································(12分) 3.(解法二)??ABC?120°,?ABE?30°,∴?EBC?90°.

在Rt△EBC中,BE?BC·tanC?2?tan30°??EA1?BA1?BE?2?2323 3. ······················································(10分) 3. ?A1C1∥AB,??A1DE??A.??A1DE??A1.∴ED?EA1?2?23·································································(12分) 3.(其它解法可参照给分)全品中 考网

26.(1)解:由

23x?83?A点坐标为??4,?0,得x??4. 0?.?B点坐标为?8,0?.由?2x?16?0,得x?8.

∴AB?8???4??12. ····················································································(2分)

28?y?x?,?x?5,?6?.由?解得∴C点的坐标为?5,·····································(3分) 33?y?6.??y??2x?16.?∴S△ABC?12AB·yC?12?12?6?36. ···························································(4分)

23?8?83?8.

?yD? (2)解:∵点D在l1上且xD?xB?8,8?. ∴D点坐标为?8, ·······················································································(5分)

??2xE?16?8.?xE?4.又∵点E在l2上且yE?yD?8,

8?.∴E点坐标为?4, 全 ·················································································(6分)

∴OE?8?4?4,EF?8.············································································(7分)

(3)解法一:①当0≤t?3时,如图1,矩形DEFG与△ABC重叠部分为五边

形CHFGR(t?0时,为四边形CHFG).过C作CM?AB于M,则Rt△RGB∽Rt△CMB.

yyl2 l2yE C D R l1E D C - 11 -R l1E l2 D C l1A O F M G B x (图1)

A F O G M (图2)

B x R F A G O M B x (图3)

BGBM?RGCM即,t3?RG6∴RG?2t. ,?Rt△AFH∽Rt△AMC,

∴S?S△ABC?S△BRG?S△AFH?36?即S??

43t?212?t?2t?12 ?8?t???8?t?.32163t?443 ····································································(10分) .- 12 -

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