Geometry Foundations

Point

A location without size, represented by a capital letter (e.g., point A).

Line

An infinite collection of points extending in one dimension, named using two points or a lowercase letter (e.g., line m).

Plane

A flat surface extending indefinitely in two dimensions, named by three noncollinear points or a capital script letter (e.g., plane P).

Ray

Has one endpoint and extends indefinitely (e.g., ray AB).

Angle

Formed by two noncollinear rays sharing a common endpoint, measured in degrees (e.g., ∠B, ∠ABC).

Parallel Lines

Lines in the same plane that do not intersect, denoted as a ∥ b.

Perpendicular Lines

Lines that intersect at right angles (90 degrees).

Circle

Defined by a center point and radius, named (e.g., circle P or ⊙P).

Postulates

Accepted facts that require no proof (e.g., through any two points, there is exactly one line).

Theorems

Statements needing proof (e.g., the Pythagorean theorem: $a^2 + b^2 = c^2$).