1 / 6

Algebraic Proof for the Pythagorean theorem

Algebraic Proof for the Pythagorean theorem. 2009-2010 5 th Hr. T he area of each of these four triangles is given by an angle corresponding with the side of length C. ½ AB.

ryann
Download Presentation

Algebraic Proof for the Pythagorean theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algebraic Proof for the Pythagorean theorem 2009-2010 5th Hr

  2. The area of each of these four triangles is given by an angle corresponding with the side of length C. ½AB

  3. Because both the A-side angle and B-side angle of each triangle are complementary angles, therefore each of the angles of the blue area in the middle is a right angle, making this area a square with side length C. The area of this square is C2 . 4(1/2 AB)+C2

  4. The large square has sides of length A + B, we can also calculate its area as (A + B)2, which expands to A2 + 2AB + B2. A2 + 2AB + B2 =4(1/2 AB)+C2

  5. (After the distribution of the 4) A2 + 2AB + B2 =2AB)+C2

  6. (after subtraction of the 2AB) A2 +B2 = C2

More Related