Q: Which object models a plane in Euclidean geometry?

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The geometry of similarity in the Euclidean plane or Euclidean space.

point, line and plane

yes, a square can only exist on a plane in euclidean geometry.

In Euclidean plane geometry every triangle MUST BE coplanar.

No, not in plane (Euclidean) geometry.

Related questions

The geometry of similarity in the Euclidean plane or Euclidean space.

Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few

Geometry that is not on a plane, like spherical geometry

Geometry that is not on a plane, like spherical geometry

Not in plane Euclidean geometry.

a plane

point, line and plane

yes, a square can only exist on a plane in euclidean geometry.

In Euclidean plane geometry every triangle MUST BE coplanar.

No, not in plane (Euclidean) geometry.

In Euclidean geometry point, line and plane are not defined.

Assuming you are referring to a triangle. In Euclidean, or plane geometry, always to 180 degrees. In non-Euclidean geometry either more or less than 180 degrees.