Precise Geometric Definitions from Undefined Terms - Geometry

All points on line $AB$ starting at $A$ and passing through $B$. A ray has one endpoint and extends infinitely in one direction.

An angle with measure greater than $0^\circ$ and less than $90^\circ$. Acute angles are smaller than right angles.

Obtuse angle. An angle greater than $90°$ but less than $180°$ is obtuse.

Acute angle. An angle less than $90°$ is acute by definition.

The common endpoint $B$ of the two rays. The vertex is always the middle letter in angle notation.

All points on line $AB$ starting at $A$ and passing through $B$. A ray has one endpoint and extends infinitely in one direction.

The points $A$ and $B$. The endpoints are the boundary points that define the segment.

All points on the line between $A$ and $B$, including $A$ and $B$. It includes all points between and including the two endpoints.

The length measured along a circle between two points on it. This undefined notion measures length following the curved path of a circle.

The length of the segment between two points on a line. This undefined notion measures the shortest path between two points on a line.

A straight path extending without end in two directions. Another fundamental undefined term that extends infinitely in both directions.

A location with no size; it has position only. It's a fundamental undefined term that establishes position without dimension.

A figure formed by two rays with a common endpoint. The angle is formed by the union of two rays sharing a common endpoint.

Correct: Parallel lines are coplanar lines that do not intersect. The error confuses parallel with perpendicular line definitions.

The rays $BA$ and $BC$. The sides are the two rays that form the angle.

All points at a fixed distance from a fixed point (the center). Every point on the circle is equidistant from the center.

The center. The center is the reference point from which all distances are measured.

The radius. The radius determines the size of the circle.

Lines that intersect to form a right angle. A right angle is formed when two lines meet perpendicularly.

Coplanar lines that do not intersect. Parallel lines maintain constant distance and never meet.

They lie in the same plane. Coplanar means the lines exist within the same geometric plane.

An angle measuring $90^\circ$. A right angle is exactly one-quarter of a full rotation.

An angle with measure greater than $0^\circ$ and less than $90^\circ$. Acute angles are smaller than right angles.

An angle with measure greater than $90^\circ$ and less than $180^\circ$. Obtuse angles are larger than right angles but less than straight angles.

An angle measuring $180^\circ$. A straight angle forms a straight line.

An angle measuring $360^\circ$. A full rotation returns to the starting position.

The distance along the line from point $A$ to point $B$. Segment length uses the undefined notion of distance along a line.

$B$ is between $A$ and $C$ if $AB + BC = AC$. This defines "between" using the additive property of distances.

$AB + BC = AC$. The segment addition postulate defines the between relationship.