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Question

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 $\stackrel{\to }{AB}$ is the same as the ray $\stackrel{\to }{BA}$. (v) The line segment $\overline{AB}$ is the same as the line segment $\overline{BA}$. (vi) The line $\stackrel{↔}{AB}$ is the same as the line $\stackrel{↔}{BA}$. (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.

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Solution

(i) False A point does not have any length, breadth or thickness. (ii) False A line segment has a definite length. (iii) False A ray has no definite length. (iv) False Ray AB has initial point A and is extended endlessly towards B, while ray BA has initial point B and is extended endlessly towards A. (v) True This is because both the line segments have definite length with end points A and B. (vi) True This is because it neither has a definite length nor any end point. (vii) True Only one line segment can pass through the two given points. (viii) True (ix) False Two intersecting planes intersect at a line. (x) False Different set of collinear points need not be collinear. (xi) False With point P, endless rays (like PA, PB, PC, PD, PE, PF) can be drawn. (xii) True Two points define one unique line. (xiii) True

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