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学习了三角形三边关系定理以后,我们知道:三角形任何一边大于其他两边的差,小于其他两边的和.三角形三边之间的这一关系, 在解题中有着较为重要的应用. 一、己知三条线段.判断三角形的构成问题解这种问题,我们只要考虑已知线段中较短的两条线段a、b的和是否大于最长的线段c即可.因为最长的线段c与较短的线段a或b的和一定大于b或a. 例1 有下列长度的三条线段能否构成三角形的三条边,为什么? (1)7,8,9 (2)3,5,8 (3)4,6,11 解 (1)能构成,因为7+8>9.
After learning the triangle trilateral relations theorem, we know that: any side of the triangle is greater than the difference between the other two sides, less than the sum of the other two sides. The relationship between the three sides of the triangle, in the problem solving has a more important application. Know the three line segments. Judging the composition of the triangle To solve this problem, we only need to consider whether the sum of the shorter two line segments a and b in the known line segment is greater than the longest line segment c. Because the longest line segment c and The sum of the short lines a or b must be greater than b or a. Example 1 Can three lines with the following length form the three sides of a triangle, and why? (1) 7,8,9 (2)3,5,8 (3 ) 4,6,11 Solutions (1) can be constructed because 7+8>9.