The Pythagorean Theorem
⏱ 0:29📘 Grade 8 · Right triangles (a sneak peek for older primary pupils)
Count the little squares: on a right triangle with sides 3 and 4, 9 + 16 makes exactly 25 — the square of the long side.
The videos are narrated in Mandarin Chinese with on-screen subtitles.
📚 What you will learn
- Right triangle: a triangle with one right angle. The two sides forming the right angle are the legs; the longest side opposite it is the hypotenuse.
- Square of a number: the number times itself, e.g. 3 × 3 = 9, written 3². It is how many small squares fit in a square with that side.
- Count them: 3 × 3 = 9, 4 × 4 = 16, 5 × 5 = 25.
- The magic: 9 + 16 = 25. The two small squares together fill the big square exactly.
- Pythagorean theorem: in a right triangle, the squares of the two legs add up to the square of the hypotenuse: a² + b² = c².
- Fun fact: ancient Chinese mathematicians wrote “gou 3, gu 4, xian 5” for this same 3-4-5 triangle.
🎙️ What the video says (in Chinese)
- 小朋友们，来认识一个神奇的秘密，勾股定理！
- 看，这是直角三角形，短边分别是 3 和 4。
- 以短边为边，画两个正方形。
- 3 乘 3，9 个小方块。4 乘 4，16 个小方块。
- 斜边是 5，5 乘 5，25 个小方块。
- 神奇的事情来了！9 加 16，刚好等于 25！
- 这就是勾股定理，两条短边的平方和，等于斜边的平方！
✏️ Try it yourself
A right triangle has legs of 6 and 8. How long is the hypotenuse?
Show answer
6² + 8² = 36 + 64 = 100 = 10², so it is 10
Is a triangle with sides 5, 12 and 13 a right triangle?
Show answer
Yes: 5² + 12² = 25 + 144 = 169 = 13²
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