Pythagoras’ Theorem: Finding Missing Sides and Distance Problems | 毕达哥拉斯定理：求未知边长与距离问题

📚 Pythagoras’ Theorem: Finding Missing Sides and Distance Problems | 毕达哥拉斯定理：求未知边长与距离问题

In KS3 Cambridge Mathematics, Pythagoras’ theorem is one of the most powerful tools for solving problems involving right-angled triangles. This article reviews the theorem, shows how to find missing sides, applies it to real-life distance problems, and highlights common exam techniques.

在剑桥 KS3 数学中，毕达哥拉斯定理是解决直角三角形问题最有力的工具之一。本文复习该定理，展示如何求未知边长，将其应用于现实中的距离问题，并强调常见的考试技巧。

1. The Right-Angled Triangle and Hypotenuse | 直角三角形与斜边

In any right-angled triangle, the right angle is usually marked with a small square. The side directly opposite this right angle is called the hypotenuse.

在任何直角三角形中，直角通常用小方格标记。与这个直角直接相对的边称为斜边。

The hypotenuse is always the longest side because it faces the largest angle, the 90° angle. The two sides that form the right angle are called the legs or shorter sides.

斜边总是最长的边，因为它面向最大的角，即 90° 角。构成直角的两条边称为直角边或短边。

In diagrams, the shorter sides are often labelled a and b, while the hypotenuse is labelled c. This standard labelling makes the formula easier to remember.

在图中，短边通常标记为 a 和 b，斜边标记为 c。这种标准标记使公式更容易记忆。

2. Statement of Pythagoras’ Theorem | 毕达哥拉斯定理的表述

Pythagoras’ theorem states that in a right-angled triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides.

毕达哥拉斯定理指出，在直角三角形中，以斜边为边长的正方形面积等于以另外两条边为边长的正方形面积之和。

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com