勾股定理神秘而美妙，它的证法多种多样，下面是教材中介绍的一种拼图证明勾股定理的方法．先做四个全等的直角三角形，设它们的两条直角边分别为a，b，斜边为c，然后按图1的方法将它们摆成正方形．

由图1可以得到（a+b）²=4× $\frac{1}{2}$ ab+c²

整理，得a²+2ab+b²=2ab+c²．

所以a²+b²=c²．

如果把图1中的四个全等的直角三角形摆成图2所示的正方形，请你参照上述方法证明勾股定理．

The teacher stood before his class of 30 students and was going to hand out the final exam papers．“I know how hard you have all worked to get ready for this test．” he said．“And because I know you are all able to understand these questions．I am ready to offer a B to anyone who would prefer not to take the test．’’
A number of students jumped up to thank the teacher and left the classroom．The teacher looked at the rest students and said．“Does anyone else want to get a B? This is your last chance．”Two more students decided to go．Seven students stayed．The teacher then handed out the papers．There were only three sentences on the paper： Congratulations! You have received an A in this class．Keep believing in yourself．
I never had a teacher who gave a test like that．but I think that it is a test that any teacher could and should give．Students who do not have confidence in what they have learned are B students at most．
The same is true for students in real life．The A students are those who believe in what they are doing because they have learned from both successes and failures．They have learned life’ s lessons, whether from school education or from events in their lives，and have become better people．Scientists say that by the age of eight，80% of what we believe about ourselves has already been formed．You are a big kid now and you realize that you have some limits(局限)．However，there is nothing you can’t do or leant to be．Sir Edmund Hillary, the first person to reach the top of Mount Qomolangma (珠穆朗玛峰)said，“We do not conquer the mountain．but ourselves．”