https://www.researchgate.net/publication/291333791_Volume_One_Geometry_without_Multiplication

Geometry-Do is now written through the red-belt level.  Can anybody here find any fault with the theorems that I have proven?  Have I omitted anything?  These theorems should include everything about triangles and parallelograms but not circles and not involving similarity or the multiplication operation.

Also, I am writing the entrance exam to become a shodan or first-degree black-belt geometer.  Can you suggest problems that are challenging but still solvable with red-belt tools?

Shodan geometry will be Book III of The Elements and extensions of Euclid's theory; Book III is mostly quadrature theory but I will include theorems about angles too.

Nidan geometry will be about the nine-point circle.

Sandan geometry I will have to consult with the masters in the field before I write about it.

Book Volume One: Geometry without Multiplication

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