⁦Axioms of solid geometry and sections⁩

⁦For the Ukrainian Grade 10 topics on the axioms of stereometry, the first facts about polyhedra and parallelism of a line and a plane⁩. ⁦Planes are named α, β, γ, and the line where two planes meet is written α ∩ β = a⁩.

Axioms: ⁦three points not on one line lie in exactly one plane; if two points of a line are in a plane, the whole line is; if two planes have a common point, they meet in a line⁩. ⁦So a line and a point outside it, or two intersecting lines, also fix a plane⁩.

⁦A line a is parallel to a plane α (a ∥ α) if they have no common point⁩. Test: ⁦if a line a that is not in α is parallel to a line b in α, then a ∥ α⁩. ⁦A section of a polyhedron is a polygon whose sides lie in the faces⁩.

⁦The planes are shown by the edges in them⁩. ⁦Turn the solid to see the hidden edges⁩.