题目

如图7，正方形ABCD的对角线相交于点O，∠CAB的平分线分别交BD、BC于E、F，作BH⊥AF于点H，分别交AC、CD于点G、P，连结GE、GF． （1）求证：△OAE ≌△OBG． （2）试问：四边形BFGE是否为菱形?若是，请证明；若不是，请说明理由． （3）试求：的值（结果保留根号）．   答案：．解：（1）证明： ∵四边形ABCD是正方形 ∴OA=OB，∠AOE=∠BOG=90°            ∵BH⊥AF ∴∠AHG=90° ∴∠GAH+∠AGH=90°=∠OBG+∠AGH ∴∠GAH=∠OBG ∴△OAE≌△OBG. （2）四边形BFGE是菱形,理由如下： ∵∠GAH=∠BAH,AH=AH, ∠AHG=∠AHB ∴△AHG≌△AHB ∴GH=BH ∴AF是线段BG的垂直平分线 ∴EG=EB,FG=FB ∵∠BEF=∠BAE+∠ABE=，∠BIt’s 2035. You have a job, a family and you’re about 40 old. Welcome to your future life. Getting ready for work, you pause in front of the mirror, “Turn red,” you say. Your shirt changes from sky blue to deep red. Tiny preprogrammed electronics are rearranged in your shirt to change its color. Looking into the mirror, you find it hard to believe that you are 40. You look much younger. With amazing advances in medicine, people in your generation may live to be 150 years old. You’re not even middle-aged. As you go into the kitchen and prepare to pour your breakfast cereal into a bowl, you hear: “To lose weight, you shouldn’t eat that,” from your shoes. They read the tiny electronic code on the cereal box to find out the nutrition details. You decide to listen to your shoes. “Kitchen, what can I have for breakfast?” A list of possible foods appear on the counter as kitchen checks its food supplies. “Ready for your trip to space. You ask your son and daughter.” In 2005 only specially trained astronauts went into space — and very few of them. Today anyone can go to space for day trips or longer vacation. Your best friend even works in space. Handing your children three strawberries each, your add, “The doctor said you need these for space travel.” Thanks to medical advices, vaccination shots are a thing of the past. Ordinary foods contain specific vaccines. With the berries in their mouths, the kids head for the front door. It’s time for you to go to work. Your car checks your fingerprints and unlocks the doors. “My office. Autopilot,” you command. Your car drives itself down the road and moves smoothly into traffic on the highway. You sit back and unroll your e-newspaper. The latest news downloads and fills the viewer. Looking through the pages, you watch the news as video films rather than read it. 1.What changes the color of your shirt? A．The mirror.        B．The counter.       C．The shirt itself.      D．The medicine. 2.How do the shoes know that your shouldn’t eat the breakfast cereal? A．By pouring the breakfast into a bowl. B．By listening to the doctor’s advice. C．By testing the food supplies in the kitchen. D．By checking the nutrition details of the food. 3.The strawberries the children eat serve as         . A．lunch            B．vaccines          C．breakfast          D．nutrition 4.How is the text organized? A．In order of time.                        B．In order of frequency. C．In order of preference.                   D．In order of importance.