Geometry Definitions

Perpendicular Lines

• Lines $l$ and $m$ are perpendicular if they intersect at a right angle.
• A less precise definition: lines meet at a single point, forming a 't' shape.

Angle

• An angle is formed by two rays sharing a common endpoint (vertex).
• The measure of an angle is the amount of turn between two straight lines with a common vertex.

Parallel Lines

• Parallel lines are distinct and can be translated onto each other (same plane, no rotation).
• Incorrect definition: Lines close together that don't intersect; parallel lines can be far apart.

Line Segment

• A line segment consists of points $p$ and $q$ (endpoints) and all points in a straight line between them.
• Incorrect definition: All points in line with $p$ and $q$ extending infinitely (that's a line).

Circle

• A circle is the set of all points in a plane equidistant from a given center point.
• A sphere is the set of all points in 3D space equidistant from a center point.
• A "perfectly round shape" lacks mathematical precision.