众所周知,直角三角形斜边上的高将直角三角形分割成的两个小直角三角形均与原直角三角形相似,从而可得赫赫有名的射影定理.本文首先给出该定理,然后举例说明其应用.定理如图1,在△ABC中,∠ACB=90°,CD上AB于点D,则有CD~2=AD·BD.AC~2=AD·4B.BC~2=BD·AB.1.直接应用例1如图2,射线AM、BN都垂直于线段AB,E为AM上一点,过点A作AC的垂线分别与BE、BN交于点F、C,过点C作AM的垂线CD,垂足为 It is well-known that the two small right-angled triangles divided by the height of the right-angled triangle on the hypotenuse of the right-angled triangle are similar to the original right-angled triangle, so that the well-known projective theorem can be obtained.This paper first gives the theorem and then illustrates its application. As shown in Fig. 1, in ABC, ∠ACB = 90 °, AB on CD is at point D, there is CD ~ 2 = AD · BD · AC ~ 2 = AD · 4B · BC ~ 2 = BD · AB.1. Direct application example 1 shown in Figure 2, ray AM, BN are perpendicular to the line segment AB, E for the AM point, the point A for the AC perpendicular to the BE, BN intersection points F, C, C for point C Vertical CD, vertical foot for