Geometry - 01.01 Lesson Flashcards

Undefined and Defined Terms

• Undefined terms are basic figures not defined by other figures; key undefined terms are point, line, and plane.
• Defined terms are explained using undefined terms or other defined terms.

Points

• A point represents a location in space and has no dimension (size).
• Points are named using capital letters, e.g., Point A or Point X.

Lines

• A line is an undefined term characterized as a straight path with no thickness, extending infinitely.
• A line has one dimension: length.
• Lines are named by two or more points on the line or a lowercase script letter (e.g., line m or line AD).

Collinear and Noncollinear Points

• Collinear points lie on the same line, indicated by the prefix "co-" (together) and "linear" (line).
• Noncollinear points do not lie on the same line.

Planes

• A plane is a flat surface extending indefinitely in all directions.
• A plane has two dimensions: length and width.
• It's named by a single letter (e.g., plane m) or three non-collinear points (e.g., plane ABC).

Points in Relation to Planes

• Coplanar points lie on the same plane.
• Noncoplanar points do not lie on the same plane.

Geometry

• The term geometry derives from "geo" (earth) and "metri" (to measure), meaning "earth measuring."

Line Segments and Rays

• A line segment is a defined term with two endpoints, containing all points between them.
• A ray has one endpoint and extends infinitely in one direction.

Angles

• An angle comprises two rays with a common endpoint, separating a plane into interior and exterior parts.
• Angles are named by placing the vertex between two letters (e.g., ∠ABC) or just naming the vertex (e.g., ∠B).

Circles

• All points on a circle are at a fixed distance (radius) from a center point.

Postulates and Theorems

• Postulates are accepted facts that do not need proof (e.g., two distinct points determine a unique line).
• Theorems are statements that can be proven using postulates and definitions; they must be demonstrated rather than assumed.