# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [Pythagorean theorem: a proof by dot products in the coordinate model](/en/derivations/derivation-mko-euclid-pythagorean-theorem-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-euclid-pythagorean-theorem)

In the Euclidean plane represented by ℝ² (with Euclidean length as distance), prove: for every right triangle ABC with the right angle at C, legs of lengths a=d(C,B) and b=d(C,A), and hypotenuse of length c=d(B,A), a²+b²=c². Then check the example C=(1,2), B=(4,6), A=(−7,8) (25+100=125), and use the non-right triangle E=(0,0), F=(4,0), H=(1,2) to show that without a right angle the relation fails in general.

Pythagorean theorem

derivation-mko-euclid-pythagorean-theorem-01





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