- Definition
In a triangle with a perfect square corner (a right angle), if you square the lengths of the two shorter sides and add them together, you'll get the square of the longest side (called the hypotenuse).
In a right triangle with sides of 3 cm and 4 cm, the hypotenuse is 5 cm because 3² + 4² = 5² (or 9 + 16 = 25).
How to teach this in 30 seconds
Try this analogy: The Pythagorean relationship is like knowing the big square tile on the slanted side of a triangular corner is the same size as the two smaller square tiles on the straight sides combined.
Ask your child: If you walk 3 blocks east and 4 blocks north, what's the shortcut distance back home?
Common mix-up: Kids often think you just add the two shorter sides to find the long one (a + b = c). The relationship is about the areas of squares on the sides, so you must square the lengths first: a² + b² = c².
Examples
- A right triangle with sides 5 cm and 12 cm has a hypotenuse of 13 cm, since 5² + 12² = 13² (25 + 144 = 169).
- Finding the length of a diagonal line across a rectangular screen that is 12 inches wide and 9 inches tall.
Pythagorean relationship is a term used in Ontario’s Kindergarten to Grade 8 curriculum.
Where this shows up
The descriptions on this page are SmartStudy’s own original, plain-language writing — not the Ministry’s wording. They are aligned to the Ontario Curriculum, © King’s Printer for Ontario. For the Ministry’s official wording, see the source link below. SmartStudy is an independent service and is not affiliated with, endorsed by, or sponsored by the Government of Ontario or the Ministry of Education. Ontario Curriculum and Resources ↗
