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几何习题,真是浩如烟海,但只要留意,就会发现有些题目是由某题演变而得。本文举出两例。作为培养学生的创造能力及研究问题能力的参考。例1 在△ABC(AB>AC)的边AB上取一点D,在边AC上取一点E,使AD=AE,直线DE和BC的延长线交于点P。求证BP:CP=BD:CE。(初级中学课本《几何》第二册66页7题) 证一过C作CF∥AB交DP于F。则BP:CP=BD:CF,∠1=∠CFE。又AD:AE,∴∠1=∠2,从而∠CEF=∠CFE,CF=CE。故BP:CP=BD:CE。证二利用梅涅
Geometry exercises are really huge, but as long as you pay attention, you will find that some topics evolved from certain questions. This article cites two cases. As a reference to develop students’ creative abilities and research problem abilities. Example 1 Take a point D on the side AB of △ABC(AB>AC) and take a point E on the side AC so that AD=AE, and the extension lines DE and BC intersect at the point P. Prove BP:CP=BD:CE. (In the junior high school textbook “Geometry” Volume II, page 66, 7 questions) The certificate is C for CF∥AB and DP is for F. Then BP:CP=BD:CF, ∠1=∠CFE. Also AD:AE, ∴∠1=∠2, thus ∠CEF=∠CFE, CF=CE. Therefore BP:CP=BD:CE. The second use of Mein