相似 (幾何)

相似三角形

數學上,相似(英语:Similar)指两个图形形状完全相同。

嚴格來說,若存在兩個點的集合,其中一個能透過放大縮小、平移旋轉或轴对称等方式變成另一個,就說它們相似

相似多边形的对应角相等,对应边成比例。

兩個圖形相似,可以以一個「~」符號連接它們,例如若三角形ABC和DEF相似便可這樣表示:

全等的图形一定相似。

三角形相似的条件

  • 兩個对应相等,两个三角形相似(AA)
  • 三個对应比例,两个三角形相似(3 sides proportional)
  • 兩個对应边成比例且其夾角相等,两个三角形相似(ratio of two sides, inc. ∠)
  • 在直角三角形中,一条对应斜边和一条对应直角边成比例,两个三角形
  • 三個对应邊平行,两个三角形相似

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