用构造三角形的方法解决几何问题,是十分常见的一种技巧,本文试分类例说如下.一、构造等边三角形例1如图1,在四边形ABCD中,∠ABC=30°,∠ADC=60°,AD=DC.求证:BD2=AB2+BC2.分析题中有30°与60°的角,而且所求证的结论形同勾股式,于是想到了利用直角三角形.因为∠CBA=30°,所以 It is a very common technique to solve the geometric problem by constructing triangles. The example of this paper is as follows. 1. Constructing an equilateral triangle Example 1 As shown in Figure 1, in quadrilateral ABCD, ∠ABC=30°, ∠ADC= 60°, AD=DC. Proof: BD2=AB2+BC2. There are 30° and 60° angles in the analysis, and the conclusion of the proof is similar to that of the Gothic type. Therefore, the use of right angle triangles was thought. Because of ∠CBA=30. and so