题干

问题1:在数学课本中我们研究过这样一道题目:如图1,∠ACB=90°,AC=BC,BE⊥MN,AD⊥MN,垂足分别为E、D.图中哪条线段与AD相等?并说明理由.

问题2:试问在这种情况下线段DE、AD、BE具有怎样的等量关系?请写出来,不需要说明理由.

问题3:当直线CE绕点C旋转到图2中直线MN的位置时,试问DE、AD、BE具有怎样的等量关系?请写出这个等量关系,并说明理由.

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答案(点此获取答案解析)

解:(1)AD=EC;

理由:∵AD⊥MN,BE⊥MN,

∴∠ADC=∠BEC=90°,

∵∠ACB=90°,

∴∠ACD+∠BCE=90°,∠DAC+∠ACD=90°,

∴∠DAC=∠BCE,

∵∠ADC=∠BEC,AC=BC,

∴△ADC≌△CEB,

∴AD=EC;

2)DE+BE=AD;

3)DE=AD+BE.

理由:∵BE⊥BC,AD⊥CE,

∴∠ADC=90

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Why I Love Cycling

    One of the first things I did when I moved to a new city was hire a bike. Why?____ You travel much faster than on foot and you notice so much more of your surroundings than when in a bus or a car. It's more appealing to wander down small streets if they seem interesting, as you can quickly get back to the main road.

    Besides, I soon discovered plenty more benefits to cycling.

    A bike means that fewer places, especially in a small city like the one where I live now, feel far away. For example, cycling to work takes me half the time that it would to walk.____

    Of course, there are obvious health benefits of cycling—a bit of extra movement as part of your daily routine can help you keep fit and healthy. Cycling on my way to work also makes me feel more energetic in the mornings.

    ____ While cars pollute the environment, bikes are carbon-neutral. Furthermore, thanks to being petrol-free, bikes are cheaper to run, buy and fix than cars. Even if you don 'town a car, a bike can pay for itself when compared to the price of bus tickets.

    ____ Always wear a helmet, pay attention to other traffic and don't forget your lights at night. Make sure you know the road rules, especially in a new place. Some cities are more cycle-friendly than others.____ Luckily, where I live now is pretty easy to ride a bike around, thanks to having lots of cycle lanes and not too many hills!

A. However, be careful when cycling.

B. I have to learn to ride safely on the right of the road.

C. Importantly, cycling also helps to reduce your carbon footprint.

D. And sometimes city roads are difficult or unpleasant for cyclists.

E. Riding a bike also means you're not restricted by bus timetables.

F. Seeing a city by bike is ideal for settling in and learning your way around.

G. Cycling to work excellently fits for someone who wants to save their pocket money.