Bhaskara's proof of the Pythagorean theorem | Geometry | Khan Academy | Summary and Q&A

179.6K views
November 28, 2012
by
Khan Academy
YouTube video player
Bhaskara's proof of the Pythagorean theorem | Geometry | Khan Academy

TL;DR

Bhaskara's proof of the Pythagorean Theorem using squares and triangles.

Install to Summarize YouTube Videos and Get Transcripts

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.

Share This Summary 📚

Summarize YouTube Videos and Get Video Transcripts with 1-Click

Download browser extensions on:

Explore More Summaries from Khan Academy 📚

Summarize YouTube Videos and Get Video Transcripts with 1-Click

Download browser extensions on: