Question

Which of the following statements is incorrect?
A) Line $\overline {AB} $ is the same as line $\overline {BA} $.
B) Line segment $\overline {AB} $ is the same as line segment $\overline {BA} $.
C) Ray \[\overrightarrow {AB} \] is the same as ray $\overrightarrow {BA} $.
D) AB perpendicular to CD is the same as CD perpendicular to AB.

Answer 1

Hint: We will first inspect all the statements one by one and draw diagrams for each of the options to observe things closely and carefully. After that, we will see which does not seem to be right will be the required answer.

Complete step-by-step answer:
We have four options with us. Let us look at them one by one.
Option A: Line $\overline {AB} $ is same as line $\overline {BA} $

In this picture, we have line AB which goes up to infinity. We cannot draw infinitely, therefore, we terminate it on the random points A and B, but it goes endlessly in both directions. So, line $\overline {AB} $ will be the same as line $\overline {BA} $, because they will give us the same line as above.
Hence, option (A) is correct.
Option B: Line segment $\overline {AB} $ is same as line segment $\overline {BA} $

In this picture, we have line AB which goes up to infinity. We cannot draw infinite, therefore, we terminated it on the random points A and B, but it goes endlessly in both the direction but the line segment AB lies between the points A and B. So, Line segment $\overline {AB} $ is same as line segment $\overline {BA} $.
Hence, option (B) is correct.
Option C: Ray \[\overrightarrow {AB} \] is same as ray $\overrightarrow {BA} $

Here, we have two rays \[\overrightarrow {AB} \] and $\overrightarrow {BA} $, we see that these both are different. As ray \[\overrightarrow {AB} \] is fixed from A and extends up to infinity at B whereas ray $\overrightarrow {BA} $ is fixed at B and extends up to infinity at A.
Hence, option (C) is incorrect.
Option D: AB perpendicular to CD is same as CD perpendicular to AB
If one line is right angled to another, it is obvious that the second line is also at right angle to the first line. Let us understand this by the following picture.

We see that both lines are mutually perpendicular to each other.

Hence, option (D) is correct.

Additional Information: A line is a 1-dimensional geometrical shape which is continuous, straight and has no end (goes up to infinity on both sides).
A line segment is a part of the line. The line when defined between two points like A and B in the figure and the portion of line between those points is known as line segment.
A ray is a type of line which has one endpoint and it extends up to infinity at the other end.
Perpendicular means on the right angle. If two lines are perpendicular to each other, it means that they are inclined at right angles to each other.

Note: The students must note that they should always try to do such kinds of questions using illustrations and pictures to get a better and clear view.
The students most of the time get confused between the difference of line, line segment and ray which eventually will lead to mistakes in such questions. You must know the differences between all of these.