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在证明平面几何题时,正确地添设辅助线,往往是关键。关于辅助线,通常有直线(包括线段、射线、平行线、垂线、圆的切线等等),和圆。对于前者,已普遍引起人们的注意、研究和运用。本文举例说明在平面几何证题中添设辅助圆的问题供老师们在教学中参考。 [例1]在四边形ABCD中,AB∥CD,BC=b,AB=AC=AD=a,求BD的长。分析:从本题AB=AC=AD=a这个条件,不难想到:B、C、D三点应在以点A为圆心,以a长为半径的圆上,若将此圆画出,本题将迎刃而解。解:以A为圆心a长为半径画圆,如图1 ∵ AB=AC=AD=a 故 B、C、D三点在⊙A上。
Accurately adding auxiliary lines is often the key when proving plane geometry problems. With regard to auxiliary lines, there are usually straight lines (including line segments, rays, parallel lines, vertical lines, round tangents, etc.), and circles. The former has generally attracted people’s attention, research and application. This article illustrates the problem of adding auxiliary circles in plane geometry test questions for teachers’ reference in teaching. [Example 1] In quadrilateral ABCD, AB∥CD, BC=b, AB=AC=AD=a, find the length of BD. Analysis: From the condition of this question AB=AC=AD=a, it is not difficult to think: B, C, and D should be centered on point A and circled by a long radius. If this circle is drawn, the problem Will be solved. Solution: Draw a circle with A as the radius of circle A, as shown in Figure 1. ∵ AB=AC=AD=a So B, C, and D are on A.