What are the undefined notions?
Option #1: point, line, distance along a line, and distance around a circular arc
Option #2: arc, parallel lines, perpendicular lines, and angle
Option #3: distance along a line, distance around a circular arc, angle, and arc
Option #4: line segment, angle, point, and arc
Option #2: arc, parallel lines, perpendicular lines, and angle
The undefined notions in geometry are fundamental concepts that cannot be precisely defined, but are understood intuitively.
Option #2: arc, parallel lines, perpendicular lines, and angle
The undefined notions are the fundamental concepts in geometry that are not defined in terms of other concepts. These notions serve as the starting points of geometric reasoning. To determine which option correctly lists the undefined notions, we need to understand the definitions of the given terms.
Option #1:
- Point: A point is a location in space, and it is considered to be a basic concept in geometry.
- Line: A line is an infinite set of points that extends indefinitely in both directions. It is also an undefined notion.
- Distance along a line: This term is not necessarily an undefined notion since distance can be defined as the length between two points on a line.
- Distance around a circular arc: This term is not necessarily an undefined notion since the distance around a circular arc can be defined as the length of the curve.
Option #2:
- Arc: An arc is a part of a curve connecting two endpoints. It is usually defined using the concept of an angle.
- Parallel lines: Two lines are parallel if they never intersect. This concept is also an undefined notion.
- Perpendicular lines: Two lines are perpendicular if they intersect at right angles. This concept is also an undefined notion.
- Angle: An angle is formed by two rays with a common endpoint. It is considered to be an undefined notion.
Option #3:
- Distance along a line: Same as in Option #1.
- Distance around a circular arc: Same as in Option #1.
- Angle: Same as in Option #2.
- Arc: Same as in Option #2.
Option #4:
- Line segment: A line segment is a part of a line that has two endpoints.
- Angle: Same as in Option #2.
- Point: Same as in Option #1.
- Arc: Same as in Option #2.
Based on the definitions, Option #2 correctly lists the undefined notions: arc, parallel lines, perpendicular lines, and angle.