△ 相似三角形计算器（比例因子、求未知边、面积比）Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio)

使用说明与常见问题How-to & FAQ

「相似三角形计算器（比例因子、求未知边、面积比）」是什么？What is the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) tool?

已知一对对应边 a 和 a′，求比例因子 k = a′/a，再求另一条边的对应边；或输入两个三角形的三条边，检验是否相似（SSS），并给出比例因子、周长比和面积比（k²）。本地处理。From one pair of corresponding sides a and a′ get the scale factor k = a′/a and the matching side for another side; or enter all three sides of both triangles to test similarity (SSS) and get the scale factor, perimeter ratio and area ratio (k²). Processed locally.

如何使用「相似三角形计算器（比例因子、求未知边、面积比）」？How do I use the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) tool?

在「相似三角形计算器（比例因子、求未知边、面积比）」中，填写「用法」、「a」、「a'」、「b」、「b'（留空则求）」等参数，结果会随输入实时计算并显示在下方。In the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio): Fill in "Use", "a", "a'", "b", "b' (blank to solve)"; results are recalculated instantly as you type.

相似三角形的边有什么关系？How are the sides of similar triangles related?

对应边成比例：a′/a = b′/b = c′/c = k，k 称为比例因子。已知一对对应边就能求出所有其他边。Corresponding sides are in proportion: a′/a = b′/b = c′/c = k, the scale factor. One known pair gives every other side.

面积比是多少？What is the area ratio?

相似三角形的周长比等于 k，面积比等于 k²。边长放大 2 倍，面积放大 4 倍。The perimeter ratio is k and the area ratio is k², so doubling the sides makes the area four times larger.

怎么判断相似？How do I tell whether triangles are similar?

三种常用判定：三边成比例 (SSS)、两边成比例且夹角相等 (SAS)、两角相等 (AA)。本页用三边检验。Three common tests: all three sides in proportion (SSS), two sides in proportion with equal included angles (SAS), or two equal angles (AA). This page uses SSS.

能举个计算实例吗？Can you show a worked example?

例如在「相似三角形计算器（比例因子、求未知边、面积比）」中填 用法 = 求未知边，a = 3，a' = 6，b = 4，结果区显示：b'：8；比例因子 k = a′/a：2；面积比 k²：4；计算：b' = b × a′/a = 4 × 6 / 3For example, entering Use = Find a missing side, a = 3, a' = 6, b = 4 in the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) gives: b': 8; Scale factor k = a′/a: 2; Area ratio k²: 4; Calculation: b' = b × a′/a = 4 × 6 / 3

哪些输入会被检查？Which inputs are validated?

「相似三角形计算器（比例因子、求未知边、面积比）」会检查这些输入——「a」、「a'」、「b」：所选方式用到时必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) checks its inputs — "a", "a'", "b": required when the chosen option uses it, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「相似三角形计算器（比例因子、求未知边、面积比）」的设置：「用法」可选 求未知边、三边检验相似（默认 求未知边）；「a」默认 3；「a'」默认 6；「b」默认 4；「b'（留空则求）」可留空；「三角形 1 三边」默认 3 4 5；「三角形 2 三边」默认 6 8 10。每次生成结果都按当前设置处理。Settings in the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) — "Use": Find a missing side, Test similarity by three sides (default Find a missing side); "a" default 3; "a'" default 6; "b" default 4; "b' (blank to solve)" optional; "Triangle 1 sides" default 3 4 5; "Triangle 2 sides" default 6 8 10. The result always uses the current settings.

计算精度如何？How precise are the results?

「相似三角形计算器（比例因子、求未知边、面积比）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「相似三角形计算器（比例因子、求未知边、面积比）」免费吗？需要注册吗？Is the Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) free? Do I need an account?

「相似三角形计算器（比例因子、求未知边、面积比）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Similar Triangles Calculator (Scale Factor, Missing Sides, Area Ratio) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.