Which of the following statements is not true ?

Question

Accepted Answer

Option 4 is the correct answer because it states that a line segment shows the maximum distance between two points, which is not true. A line segment is simply the shortest path connecting two points on a plane. It does not represent the maximum distance, as there can be other paths or curves that extend beyond the line segment between the same two points.

Let's examine why the other options are true:

1. **Option 1: Point is a sign, which has no size.**
   - A point is a fundamental concept in geometry that represents a location in space. It has no dimensions—no length, width, or height—hence it has no size. It is simply a position or location marker.

2. **Option 2: Line is endless in both directions.**
   - A line is defined as a straight one-dimensional figure having no thickness and extending infinitely in both directions. This is a fundamental property of lines in geometry, distinguishing them from line segments and rays.

3. **Option 3: Line segment is a part of a line, that is bounded by two points.**
   - A line segment is indeed a portion of a line that is bounded by two distinct endpoints. It has a definite length, unlike a line, which extends infinitely.

In summary, Option 4 is not true because a line segment does not show the maximum distance between two points; it represents the shortest distance. The other options correctly describe the properties of points, lines, and line segments in geometry.