英文摘要.doc

Angles and Sides of Triangles 1. The basic nature of the triangle 1 Length of sides : In any triangle , each side is shorter than the sum of the lengths of the other two sides Inference: the difference between both sides ofa triangle is less than the third side. 2 Angle measures : In any triangle, the sum of the three interior angles is 180 °. 3 Angle and opposite sides : In any triangle, the relative angle sizes correspond to the relative lengths of the sides opposite those angles. In other words, the smaller the angle, the smaller the side opposite the angle ( and vice-versa ). Accordingly, if two angles are equal in size, the sides opposite those angles are of equal length ( and vice-versa ). Inference: Ⅰ. Triangle, if the smallest sum of squares of the two sides is less than the third side of the square, and, this triangle will be an obtuse triangle. Ⅱ. Triangle if two sides of the square of the smallest and greater than the third side of the square and, this triangle will be an acute angle triangle 4 Area ofa triangle : The area of any triangle is equal to 1/2 the product of its base and its height ( height is also called the altitude ):?? 1 1 2 2 Area base altitude height bh ? ? ? ? In that triangle where the length of three sides can use a special formula to solve the triangle area. Length of its sides of the triangle is , , , 2