# Geometry Foundations to the Pythagorean Theorem

Move from the language of points, lines, and planes through triangles, angles, length, and right triangles to the Pythagorean theorem.

This is a suggested learning sequence, not a universal logical dependency or a formal proof.


- Stage 1 · required



## [Points, lines, and planes](/en/mko/mko-point-line-plane/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

First distinguish geometric positions, extended objects, and their diagrams.

[Related questions](/en/explore/?mko=mko-point-line-plane) [Concept guides](/en/derivations/?q=mko-point-line-plane)


- Stage 2 · required



## [Triangle](/en/mko/mko-triangle/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

Build a triangle, its vertices, and its sides from three distinct noncollinear points.

[Related questions](/en/explore/?mko=mko-triangle) [Concept guides](/en/derivations/?q=mko-triangle)


- Stage 2 · required



## [Angle](/en/mko/mko-angle/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

Establish the language of two rays with a common endpoint and angle measure.

[Related questions](/en/explore/?mko=mko-angle) [Concept guides](/en/derivations/?q=mko-angle)


- Stage 2 · required



## [Euclidean length](/en/mko/mko-euclidean-length/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

In parallel, establish the meaning of side length and distance.

[Related questions](/en/explore/?mko=mko-euclidean-length) [Concept guides](/en/derivations/?q=mko-euclidean-length)


- Stage 3 · required



## [Right triangle](/en/mko/mko-right-triangle/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

Use a right angle and sides to identify the geometric object to which the theorem applies.

[Related questions](/en/explore/?mko=mko-right-triangle) [Concept guides](/en/derivations/?q=mko-right-triangle)


- Stage 4 · required



## [Pythagorean theorem](/en/mko/mko-euclid-pythagorean-theorem/?from=%2Fen%2Fpaths%2Fpath-geometry-foundations%2F)

Finally understand the squared relation and its proof boundaries.

[Related questions](/en/explore/?mko=mko-euclid-pythagorean-theorem) [Concept guides](/en/derivations/?q=mko-euclid-pythagorean-theorem)



Path source & statuspath-geometry-foundations · candidate

[Original paths JSON](/data/architecture/learning-paths.json)