Pythagorean Theorem — a² + b² = c²
Watch the squares fill and flow
Build squares on all three sides of a right triangle, then watch the area of the two smaller squares flow into the largest one. Change the triangle shape with the triple picker and replay the proof.
What this game shows · The Pythagorean Theorem
For any right triangle, the area of the square on the hypotenuse equals the sum of the areas on the two legs: a² + b² = c². This animation builds all three squares and watches the smaller two literally flow into the largest.
- Right triangle
- one 90° angle. Hypotenuse is opposite that angle.
- a² and b²
- squares built on the two legs.
- c²
- square on the hypotenuse — equals a² + b² for any right triangle.
Aligned with CCSS 8.G.B.6 (explain a proof of the Pythagorean theorem).
Pythagorean Theorem — Visual Proof
Watch a² + b² flow into c². Change the triangle with the buttons below.
Press Play to see the proof
Pythagorean theorem, proven.
01 What does "a² + b² = c²" really mean? Area equality
Build a square on each side of a right triangle. The big square (on the hypotenuse) has the same area as the two smaller squares combined. It is an area equality, not just a number trick.
02 Does it work for any right triangle? All right triangles
Yes. Test 3-4-5: 9 + 16 = 25 = 5². Then 5-12-13: 25 + 144 = 169 = 13². The animation lets you swap triples and watch the proof replay.
03 What if the triangle is not a right triangle? 90° required
The equation does not hold. For acute triangles, a² + b² > c². For obtuse, a² + b² < c². The "right" angle is essential.
04 Which grade is this game for? Grades 7–8
Grades 7–8, aligned with CCSS 8.G.B.6. Foundation for distance formula, trig, and complex geometry.