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.
(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.
(i) False
The given statement is false, as it is not necessary that the two lines always intersect. In the case of parallel lines, the two lines never intersect or there is no common point between them.
(ii) False
The given statement is false, as there is only one point common between two intersecting lines. So, two lines cannot intersect at two points.
(iii) False
A line segment is a part of line defined by two end points, so it is always of a definite length. Hence, the given statement is false.
(iv) True
The given statement is true as a unique line can be determined by minimum of two distinct points.
(v) False
A ray is defined as a part of the line with one end point, where the other end can be stretched indefinitely. Therefore, a ray cannot have a finite length.
(vi) True
The given statement is true as a ray is defined as a part of the line with one end point, where the other end can be stretched indefinitely.
(vii) False
A line segment is a part of line defined by two end points. So the given statement is false as a line segment has two end points.
(viii) False
While denoting a ray, the first letter denotes the end point and the second one denotes the end which can be extended. So, for ray AB, A is the end point and B is the end which can be stretched while for ray BA, B is the end point and A the end which can be stretched. Therefore, ray AB is not the same as ray BA.
(ix) False
The given statement is false as infinite number of lines can pass through a given point.
(x) False
Two lines are said to be coincident if they lie exactly on top of each other, which means that they have all the points in common. So the given statement is false.
(i) False
The given statement is false, as it is not necessary that the two lines always intersect. In the case of parallel lines, the two lines never intersect or there is no common point between them.
(ii) False
The given statement is false, as there is only one point common between two intersecting lines. So, two lines cannot intersect at two points.
(iii) False
A line segment is a part of line defined by two end points, so it is always of a definite length. Hence, the given statement is false.
(iv) True
The given statement is true as a unique line can be determined by minimum of two distinct points.
(v) False
A ray is defined as a part of the line with one end point, where the other end can be stretched indefinitely. Therefore, a ray cannot have a finite length.
(vi) True
The given statement is true as a ray is defined as a part of the line with one end point, where the other end can be stretched indefinitely.
(vii) False
A line segment is a part of line defined by two end points. So the given statement is false as a line segment has two end points.
(viii) False
While denoting a ray, the first letter denotes the end point and the second one denotes the end which can be extended. So, for ray AB, A is the end point and B is the end which can be stretched while for ray BA, B is the end point and A the end which can be stretched. Therefore, ray AB is not the same as ray BA.
(ix) False
The given statement is false as infinite number of lines can pass through a given point.
(x) False
Two lines are said to be coincident if they lie exactly on top of each other, which means that they have all the points in common. So the given statement is false.
