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Point, Lines, Plane and Solids

Write the tru...

Question

Write the truth value (T/F) of each of the following statements :

(i) Two lines intersect in a point.

(ii) Two lines may intersect in two points.

(iii) A segment has no length.

(iv) Two distinct points always determine a line.

(v) Every ray has a finite length.

(vi) A ray has one end-point only.

(vii) A segment has one end-point only.

(viii) The ray AB is same as ray BA.

(ix) Only a single line may pass through a given point.

(x) Two lines are coincident if they have only onepoint in common.

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Solution

(i) False : As two lines do not intersect also any a point.

(ii) False : Two lines intersect at the most one point.

(iii) False : A line segment has definitely length.

(iv) True.

(v) False : Every ray has no definite length.

(vi) True.

(vii) False : A segment has two end point.

(viii) False : Rays AB and BA are two different rays.

(ix) False : Through a given point, infinitely many lines can pass.

(x) False : Two lines are coincident of each and every points coincide each other.

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Similar questions

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.

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. 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. Tell which of the following statements are true (T) and which are false (F).

(i) The intersection of two segments may be a segment.
(ii) Two segments may intersect at a point which is not any end-point of either segments containing it.
(iii) Every ray is a segment.
(iv) Every segment is a ray.

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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