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Perpendiculars and Parallels

Choose the fa...

Question

Choose the false statement:
(a) Line $\overset{\leftrightarrow}{A B}$ is the same as line $\overset{\leftrightarrow}{B A}$
(b) Ray $\vec{A B}$ is the same as ray $\vec{B A}$
(c) Line segment $\bar{A B}$ is the same as teh line segment $\bar{B A}$
(d) None of these

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Solution

(b) Ray $\vec{AB} is same as ray \vec{BA}$
This is because the initial points in these rays are A and B, respectively, and are extended endlessly towards B and A, respectively.

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Similar questions

Q. Write 'T' for true and 'F' for false in case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray

\vec{A B}

is the same as the ray

\vec{B A}

.
(v) The line segment

\bar{A B}

is the same as the line segment

\bar{B A}

.
(vi) The line

\overset{\leftrightarrow}{A B}

is the same as the line

\overset{\leftrightarrow}{B A}

.
(vii) Two points A and B in a plane determine a unique line segment.
(viii) Two intersecting lines intersect at a point.
(ix) Two intersecting planes intersect at a point.
(x) If points A, B, C are collinear and points C, D, E are collineaer then the pints A,B, C, D, E are collinear.
(xi) One and only one ray can be drawn with a given end point.
(xii) One and only one line can be drawn to pass through two given points.
(xiii) An unlimited number of lines can be drawn to pass through a given point.

Q. Which of the following statements are true?
(i) A line segment has no definite length.
(ii) A ray has no end-point.
(iii) A line has a definite length.
(iv) A line

\overset{\leftrightarrow}{A B}

is same as line

\overset{\leftrightarrow}{B A}

\underset{A B}{\to}

\underset{B A}{\to}

.
(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two distinct lines cannot have more than one point in common.
(ix) Two intersecting lines cannot be both parallel to the same line.
(x) Open half-line OA is same as ray

\underset{O A}{\to}

.
(xi) Two lines may intersect at two points.
(xii) Two lines l and m are parallel only when they have no point in common.

The ray AB is same as ray BA. True or False?

Q. Write 'T' for true and 'F' for false for each of the statements given below:
(i) If two line segments do not intersect, they are parallel.
(ii) If two rays do not intersect, they are parallel.
(iii) If two lines do not meet even when produced, they are called parallel lines.
(iv) Two parallel lines are everywhere the same distance apart.
(v) A ray has a finite length.
(vi) Ray

\vec{A B}

is the same as ray

\vec{B A}

Q. Which statement is true?
(a) A line segment

A B

, when extended in both directions, is called ray

\underset{A B}{\to}

Ray \underset{A B}{\to} = ray \underset{B A}{\to}

\underset{A B}{\to}

has one end-point A.
(d) Ray

\underset{A B}{\to}

has two end-points A and B.

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