Undefined notions in geometry are basic concepts that do not have formal definitions but are understood through their common properties and relationships. In Euclidean geometry, the most commonly accepted undefined notions are "point," "line," and "plane."
Among the options provided:
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Option #1: point, line, distance along a line, and distance around a circular arc
- "Point" and "line" are undefined notions; however, "distance along a line" and "distance around a circular arc" are measurable concepts and therefore defined.
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Option #2: arc, parallel lines, perpendicular lines, and angle
- None of these are considered undefined notions in basic geometry.
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Option #3: distance along a line, distance around a circular arc, angle, and arc
- Similar to Option #2, these are all defined concepts.
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Option #4: line segment, angle, point, and arc
- "Point" is an undefined notion, but "line segment," "angle," and "arc" are all defined.
Based on this analysis, the option that best aligns with the concept of undefined notions is Option #1 since it includes "point" and "line." However, the notion of distance, while foundational, is typically defined rather than undefined.
In conclusion:
- Correct Choice: None of the options fully capture the essence, but Option #1 has the closest with point and line.