2017 · Q79
Consider the following statements in respect of three straight lines A, B and C on a plane:
- 1If A and C are parallel and B and C are parallel, then A and B are parallel.
- 2If A is perpendicular to C and B is perpendicular to C, then A and B are parallel.
- 3If the acute angle between A and C is equal to the acute angle between B and C, then A and B are parallel.
Which of the above statements are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1, 2 and 3
- B1 and 2 only
- C1 and 3 only
- D2 and 3 only
Explanation
Statements 1 and 2 are the parallel-transitivity and common-perpendicular properties — both true. Statement 3 is false: A and B could lie on opposite sides of C (e.g. C the x-axis, A at +30°, B at −30°), making equal acute angles with C yet not parallel. Hence option (B) 1 and 2 only.