利用勾股定理的逆定理,可以根据三角形的三边判别某三角形是否为直角三角形.在使用该定理时,如果把已知条件适当变形,可以化复杂为简单.一、两边同时平方例1若△ABC的三边a、b、c满足a+b=10,ab=18,c=8,试判别△ABC的形状.析解∵a+b=10,∴(a+b)2=100,∴a2+2ab+b2=100.把ab=18代入,得 By using the inverse theorem of the Pythagorean theorem, it is possible to judge whether a certain triangle is a right-angled triangle according to the three sides of the triangle. When using this theorem, if the known conditions are properly deformed, the complexity can be simplified to be simple. △ ABC on the three sides a, b, c satisfy a + b = 10, ab = 18, c = 8, try to distinguish △ ABC shape. Analyze ∵a + b = 10, ∴ (a + b) 2 = 100 , ∴ a2 +2 ab + b2 = 100. Substitute ab = 18, too