Find out the incorrect statement, if any, in the following: An angle is formed when we have (a) two rays with a common end-point (b) two line segments with a common end-point (c) a ray and a line segment with a common end-point
Incorrect: (b) and (c)
Idea: An angle is made by two rays starting from the same point.
Definition in small steps
• A ray starts at a point and goes on endlessly in one direction.
• Write a ray as \(\overrightarrow{OA}\).
• Two rays \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\) with the same start point \(O\) make an angle.
• The common start point is the vertex.
Check each statement
(a) Two rays with a common end-point
• This matches the definition exactly.
• So, (a) is correct.
(b) Two line segments with a common end-point
• A line segment \(\overline{OA}\) has two ends and a fixed length.
• By itself, a segment does not “go on forever” like a ray.
• An angle is defined using rays, not just segments.
• So, (b) is incorrect.
(c) A ray and a line segment with a common end-point
• One part is a ray, the other is only a segment.
• The definition needs two rays.
• So, (c) is incorrect.
Conclusion
Incorrect statements: (b) and (c).