Which of the following statements is false?

(a) Through a given point, only one staright line can be drawn.

(b) Through two given point, it is possible to draw one and only one straight line.

(c) Two straight lines can intersect only at one point.

(d) A line segment can intersect only at one point.

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Solution

NSWER:
(a) Through a given point, only one straight line can be drawn.
Clearly, statement (a) is false because we can draw infinitely many straight lines through a given point.

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Similar questions

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.

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

(i) Point has a size because we can see it as a thick dot on paper.
(ii) By liens in geometry, we mean only straight lines.
(iii) Two lines in a plane always intersect in a point.
(iv) Any plane through a vertical line is vertical.
(v) Any plane through a horizontal line is horizontal.
(vi) There cannot be a horizontal line a vertical plane.
(vii) All lines in a horizontal plane are horizontal.
(viii) Two lines in a plane always intersect in a point.
(ix) If two lines intersect at a point P, then P is called the point of concurrence of the two lines.
(x) If two lines intersect at a point P, then p is called the point of intersection of the two lines.
(xi) If A,B,C and D are collinear points D, P and Q are collinear, then points A, B, C, D, P and Q are always collinear.
(xii) Two different lines can be drawn passing through two given points.
(xiii) Through a given point only one line can be drawn.
(xiv) Four points are collinear if any three of them lie on the same line.
(xv) The maximum number of points of intersection of three lines is three.
(xvi) The minimum number of points of intersection of three lines is one.

Through a given point, we can draw only one perpendicular to a given line.

Harman told Kushagra that only one line parallel to a given line can be drawn through a point which is not on the line. State whether Harman's statement is true or false.

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

NSWER: (a) Through a given point, only one straight line can be drawn. Clearly, statement (a) is false because we can draw infinitely many straight lines through a given point.

NSWER:
(a) Through a given point, only one straight line can be drawn.
Clearly, statement (a) is false because we can draw infinitely many straight lines through a given point.