General Principles of Solid Geometry and Spatial Relationships

This set of vocabulary flashcards covers the fundamental definitions, theorems, and spatial relationships introduced in the spatial geometry lecture notes, including properties of lines, planes, polyhedrons, and perpendicularity/parallelism.

Solid Geometry (Đại cương Hình học không gian)

The study of points, lines, and planes in three-dimensional space, including properties of pyramids and tetrahedrons.

Line through two points

There is one and only one line that passes through two distinct points.

Plane through three points

There is one and only one plane that passes through three non-collinear points.

Line on a plane

If a line has two distinct points belonging to a plane, then every point on that line belongs to that plane.

Intersection of two planes

If two distinct planes have a common point, they also have another common point, and their intersection is a line.

Pyramid (Hình chóp)

A 3D shape formed by a convex polygon base and triangles connecting the base vertices to a common apex (S).

Tetrahedron (Hình tứ diện)

A triangular pyramid with four faces, each of which is a triangle.

Line parallel to a plane

A line d is parallel to plane (α) if d is not in (α) and is parallel to a line d' that lies within (α).

Intersection of two parallel planes

If a plane (γ) intersects two parallel planes (α) and (β), the resulting intersection lines are parallel to each other.

Skew lines (Hai đường thẳng chéo nhau)

Two lines that are not coplanar, meaning they do not lie in the same plane and do not intersect.

Prism (Hình lăng trụ)

A polyhedron with two identical parallel polygon bases and lateral faces that are parallelograms.

Line perpendicular to a plane

A line d is perpendicular to plane (P) if it is perpendicular to every line lying in (P).

Theorem of Three Perpendiculars

A theorem stating that a line b in plane (P) is perpendicular to an inclined line a if and only if b is perpendicular to the projection a' of a on (P).

Angle between a line and a plane

The angle between a line and its orthogonal projection onto the plane.

Dihedral Angle (Góc giữa hai mặt phẳng)

The angle formed by two lines, one in each plane, both perpendicular to the intersection line at the same point.

Distance from a point to a plane

The length of the perpendicular segment dropped from the point to the plane.

Rectangular Parallelepiped (Hình hộp chữ nhật)

A prism with six rectangular faces where all adjacent faces are perpendicular.

Right Prism (Lăng trụ đứng)

A prism whose lateral edges are perpendicular to its bases.

Regular Pyramid (Hình chóp đều)

A pyramid with a regular polygon base and a vertex that projects orthogonally onto the center of that base.

Skew Line Distance

The length of the unique line segment that is perpendicular to both skew lines.