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Question

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.

(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.

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Solution

(i) False

(ii) True

(iii) False

They may be parallel.

(iv) True

(v) False

In every vertical plane there must be horizontal line.

e.g.:-Intersecting line of a wall and floor of a room is horizontal line and it is also a line on the wall that is on the vertical plane.

(vi) False

Counter example:-Intersecting line of a wall and floor of a room is horizontal line and it is also a line on the wall that is on the vertical plane.

(vii) True

(viii) False

They can be parallel line also.

(ix) False

Through a point of concurrence, at least three lines should pass.

(x) True

(xi) False

Here ABCD is in one plane and DPQ may be in different plane and they may be intersecting through the point D.

(xii) False

Two lines are either intersecting at one point or they may be parallel lines or they may be coincident lines.

(xiii) False

Through a given point infinite line can be drawn.

(xiv) False

Points are collinear only if all points are in the same plane.

(xv) True

(xvi) False

Minimum number of points of intersection of three lines be zero.

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