Thousands of houses         by the floods in Guangxi last month.

—Have you heard of Earth Day?
—Yes.The first Earth Day          in 1970 to educate us to protect our planet.

Last year, Shenzhou-8         into the space. It made us proud.

—Mum, can I go to the zoo with Linda?
—When your homework       , you can.

LadyGaga is very popular, and she       by many boys and girls at school.

Today,computers are really helpful. They           everywhere.

已知:线段OA⊥OB,点C为OB中点,D为线段OA上一点.连接AC,BD交于点P.
(3)如图3,把题目中“点C为OB中点”改为“BC:CO=1:n”,当AD:DO=1:m时,求的值.

解题思路:类比第1题,第2题,过点D作DE∥OB交AC于点E,则AE和CE的数量关系是        ,EP和CP的数量关系是        ,的值是        .以上横线处,依次所填正确的是(    )

已知:线段OA⊥OB,点C为OB中点,D为线段OA上一点.连接AC,BD交于点P.
(2)如图2,当AD:DO=1:m时,求的值;

解题思路:类比第1题,过点D作DE∥OB交AC于点E,则AE和CE的数量关系是        ,EP和CP的数量关系是        ,的值是        .以上横线处,依次所填正确的是(    )

已知:线段OA⊥OB,点C为OB中点,D为线段OA上一点.连接AC,BD交于点P.
(1)如图1,当D为OA中点时,求的值;

解题思路:(1)尝试探究:在图1中,过点D作DE∥OB交AC于点E,则AE和CE的数量关系是        ,EP和CP的数量关系是        ,的值是        .以上横线处,依次所填正确的是(    )

类比延伸:把图(2)中的正方形都换成矩形,如图(3),且DA:AB=HA:AE=m:n,请探究HD:GC:EB的值.

解题思路:类比第2题,可证△ADH和△ABE的关系是        ,则HD:EB=        ;其次,连接AC,AG,则△ABC和△AEG的关系是          ,则△AGC和△AEB的关系是          ,则GC:EB=        ;最后,HD:GC:EB=              .
以上横线处,依次所填正确的是(    )
①相似;②全等;③m:n;④n:m;⑤;⑥;⑦;⑧