1 / 6

Proof of Pythagoras s Theorem

?Prove' means what exactly?. A proof in mathematics is a process of logical stepsEach step makes a statement using facts that are recognised

rangsey
Télécharger la présentation

Proof of Pythagoras s 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. Proof of Pythagoras’s Theorem GCSE Higher

    2. ‘Prove’ means what exactly? A proof in mathematics is a process of logical steps Each step makes a statement using facts that are recognised & known to be true In vast majority of cases, a proof involves some manipulation of algebra

    3. Proof of Pythagoras’ Theorem Consider this square It has side length c It’s area is thus c2

    4. Rotate the Square Surround it with another square Label Triangles’ sides a & b Now calculate area of large and small squares SHADED is c2

    5. Area Larger Square = (a + b)2 = a2 + 2ab + b2 Area of EACH small Triangle = ½ab Area of 4 small triangles = 2ab

    6. Shaded Square’s area is…… = a2 + 2ab + b2 – 2ab = a2 + b2 BUT Shaded Area is c2 SO c2 =a2 + b2

More Related