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First Four Postulates

Which of the ...

Question

Which of the following is a false statement?
(a) An infinite number of lines can be drawn through a given point.
(b) A unique line can be drawn through two given points.
(c) Ray $\underset{A B}{\to} = ray \underset{B A}{\to}$ .
(d) A ray has one end-point.

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Solution

(c) $R a y \vec{A B} = R a y \vec{B A}$

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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 is a true statement?
(a) Only a unique line can be drawn through a given point.
(b) Infinitely many lines can be drawn through two given points.
(c) If two circles are equal, then their radii are equal.
(d) A line has a definite length.

Which of the following is a true statement ?

(a) Only a unique line can be drawn to pass through a given point.

(b) Infinitely many lines can be drawn to pass through two given points.

(c) If two circles are equal,then their radii are equal.

(d) A line has a definite length.

Q. Write the turth 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 one point in common.

Q. Which of the following statements is false?
(a) Through a given point, only one straight line can be drawn.
(b) Through two given points, it is possible to draw one and only one straight line.
(c) Two straight lines can intersect at only one point.
(d) A line segment can be produced to any desired length.

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