Bhaskara's proof of the Pythagorean theorem  Geometry  Khan Academy  Summary and Q&A
TL;DR
Bhaskara's proof of the Pythagorean Theorem using squares and triangles.
Questions & Answers
Q: What is Bhaskara's proof of the Pythagorean Theorem?
Bhaskara's proof involves starting with a square and constructing four right triangles inside it, demonstrating their congruence and equal hypotenuse lengths. By rearranging the triangles, he shows how the area of the square is equal to the sum of the areas of two smaller squares, proving the Pythagorean Theorem.
Q: How does Bhaskara prove that the four triangles are congruent?
Bhaskara shows that all four triangles have the same angles  theta, 90 minus theta, and 90 degrees. Since the angles are equal, and the hypotenuses are also equal, the triangles are congruent.
Q: What is the key idea behind Bhaskara's proof?
The key idea is to rearrange the triangles inside the square, creating two smaller squares with areas equal to the areas of the triangles. By comparing the areas, Bhaskara proves the Pythagorean Theorem.
Q: What is the significance of Bhaskara's proof?
Bhaskara's proof provides an alternative method for proving the Pythagorean Theorem. It demonstrates the geometric relationship between squares and right triangles and highlights the elegance of mathematical proofs.
Summary & Key Takeaways

Bhaskara starts with a square and constructs four right triangles inside it.

He shows that these triangles are congruent and have the same hypotenuse length.

By rearranging the triangles, he proves that the area of the square is equal to the sum of the areas of two smaller squares, which leads to the Pythagorean Theorem.