在平面几何的计算题或证明题中,往往通过添加辅助线把复杂问题简化。梯形问题更是如此,常常添加适当辅助线,使其转化为三角形、平行四边形问题。下面谈谈梯形问题中几种常用的辅助线,供读者参考。 1.添对角线,割成两个三角形 例1 已知:如图(1),在梯形ABCD中,AB∥CD,ADBC=CD,∠A=60°.求证:CD=1/2AB。 分析:我们通常利用“三角形中位线定理”和在“直角三角 In the calculation or proof of plane geometry, complex problems are often simplified by adding auxiliary lines. The trapezoidal problem is even more so, often adding appropriate auxiliary lines to convert it into a triangular, parallelogram problem. Here are some commonly used auxiliary lines in the trapezoidal problem for readers’ reference. 1. Add Diagonal lines, cut into two triangles Example 1 Known: Figure (1), in the trapezoid ABCD, AB ∥ CD, ADBC ​​= CD, ∠ A = 60 °. Proof: CD = 1/2AB. Analysis: We usually use the “triangle median line theorem” and the "right angle triangle