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.
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.
Aligned with CCSS 8.G.B.6 (explain a proof of the Pythagorean theorem).
Watch a² + b² flow into c². Change the triangle with the buttons below.
Press Play to see the proof
Geometry and measurement model
Pythagorean Theorem — a² + b² = c² is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Pythagorean Theorem — a² + b² = c² helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
Learning goals
How to play
Continue with guided practice
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.
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.
The equation does not hold. For acute triangles, a² + b² > c². For obtuse, a² + b² < c². The "right" angle is essential.
Grades 7–8, aligned with CCSS 8.G.B.6. Foundation for distance formula, trig, and complex geometry.
