Pythagoras’ Theorem | 毕达哥拉斯定理

📚 Pythagoras’ Theorem | 毕达哥拉斯定理

Pythagoras’ theorem is one of the most important results in KS3 mathematics. It connects the three sides of a right-angled triangle and provides a reliable method for finding an unknown side. This article explains the theorem step by step, with worked examples and common mistakes to avoid.

毕达哥拉斯定理是 KS3 数学中最重要的结论之一。它把直角三角形三条边联系起来，并提供了一种可靠的方法来求未知边。本文逐步解释该定理，并配有解题示例和需要避免的常见错误。

1. What is Pythagoras’ Theorem? | 什么是毕达哥拉斯定理？

A right-angled triangle contains one angle of exactly 90°. The side opposite this right angle is called the hypotenuse, and it is always the longest side. Pythagoras’ theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

直角三角形包含一个恰好为 90° 的角。这个直角的对边叫做斜边，它总是最长的边。毕达哥拉斯定理指出，斜边的平方等于另外两条边的平方之和。

The theorem only applies to right-angled triangles. If a triangle does not contain a 90° angle, you cannot use the formula a² + b² = c² directly. This is the first check you should make in any question.

该定理只适用于直角三角形。如果三角形不包含 90° 角，就不能直接使用公式 a² + b² = c²。这是你在任何题目中应做的第一个检查。

a² + b² = c²

Here, c represents the hypotenuse, while a and b represent the two shorter sides. The order of a and b does not matter, but c must be the side opposite the right angle.

这里 c 表示斜边，a 和 b 表示两条较短的边。a 和 b 的顺序无关紧要，但 c 必须是直角的对边。

2. Labelling the Triangle Correctly | 正确标注三角形

Before you calculate, label the three sides. Put the right angle in the bottom left of your sketch. The side directly across from the right angle is the hypotenuse; label it c. The other two sides are labelled a and b.

计算前，先标注三条边。将直角放在草图的左下角。与直角正对的边是斜边，把它标记为 c。另外两条边标记为 a 和 b。

It is helpful to write the letters on the diagram. If you mix up the hypotenuse with a shorter side, your answer will be incorrect. Always ask: which side is opposite the 90° angle?

在图上写出字母会很有帮助。如果把斜边和较短边混淆，

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