Selina Textbook Solutions: Fundamental Concepts | Mathematics Class 6 ICSE PDF Download

 Page 1


IMPORTANT POINTS 
1. Fundamental Concepts : Geometry is the study of position,, shape, size and other 
properties of different figures. The geometrical terms such as : point, line, plane, etc., 
contain the basic ideas for the development of geometry. 
(i) Point : A point is a mark of position. It has neither length nor width nor. thickness and 
occupies no space. 
 
(ii) Line : A line has only length. It has neither width nor thickness. 
 
(iii) Ray : It is a line (i.e. a straight line) that starts from a given fixed point and moves in 
the same direction. 
 
(iv) Line Segment: A line segmeftt is a part of a straight line. A line segment is a part of 
a line and also of a ray. 
 
(v) Surface : A surface has length and width, but no thickness. 
(vi) Plane : It is a flat surface. A plane has length and width, but no thickness. 
(vii) Parallel Lines : Two straight lines are said to be parallel to each other if they lie in 
the same plane and do not meet when produced on either side. 
 
(viii)Intersecting Lines : If two lines lie in the same plane and are not parallel to each 
other, they are called intersecting lines. 
(xi) Collinearity of Points : If three of more points lie on the same straight line, then 
the points are called collinear points. 
 
(x) Concurrent Lines : If three or more straight lines pass through the same point, the 
Page 2


IMPORTANT POINTS 
1. Fundamental Concepts : Geometry is the study of position,, shape, size and other 
properties of different figures. The geometrical terms such as : point, line, plane, etc., 
contain the basic ideas for the development of geometry. 
(i) Point : A point is a mark of position. It has neither length nor width nor. thickness and 
occupies no space. 
 
(ii) Line : A line has only length. It has neither width nor thickness. 
 
(iii) Ray : It is a line (i.e. a straight line) that starts from a given fixed point and moves in 
the same direction. 
 
(iv) Line Segment: A line segmeftt is a part of a straight line. A line segment is a part of 
a line and also of a ray. 
 
(v) Surface : A surface has length and width, but no thickness. 
(vi) Plane : It is a flat surface. A plane has length and width, but no thickness. 
(vii) Parallel Lines : Two straight lines are said to be parallel to each other if they lie in 
the same plane and do not meet when produced on either side. 
 
(viii)Intersecting Lines : If two lines lie in the same plane and are not parallel to each 
other, they are called intersecting lines. 
(xi) Collinearity of Points : If three of more points lie on the same straight line, then 
the points are called collinear points. 
 
(x) Concurrent Lines : If three or more straight lines pass through the same point, the 
lines are called concurrent lines. 
 
EXERCISE 23 (A) 
Question 1. 
State, true or false, if false, correct the statement. 
(i) A dot has width but no length. 
(ii) A ray has an infinite length only on one side of it. 
(iii) A line segment PQ is written as  . 
(iv)   represents a straight line. 
(v) Three points are said to be collinear, if they lie in the same plane. 
(vi) Three or more points all lying in the same line, are called collinear points. 
Solution: 
(i) False : Because a dot has no length, no breadth. 
(ii) True. 
(iii) False : A line segment PQ is written as PQ. 
(iv) True. 
( v) False: Three points are called collinear points if they are in the same straight line. 
(vi) True. 
Question 2. 
Write how many lines can be drawn through : 
(i) a given point ? 
(ii) two given fixed points ? 
(iii) three collinear points ? 
(iv) three non-collinear points ? 
Solution: 
(i) Infinite (unlimited) line can be drawn through a given point. 
(ii) only one line can be drawn through two given point. 
(iii) only one line can be drawn through three collinear points. 
(iv) None (no) line can be drawn through three non-collinear points. 
Page 3


IMPORTANT POINTS 
1. Fundamental Concepts : Geometry is the study of position,, shape, size and other 
properties of different figures. The geometrical terms such as : point, line, plane, etc., 
contain the basic ideas for the development of geometry. 
(i) Point : A point is a mark of position. It has neither length nor width nor. thickness and 
occupies no space. 
 
(ii) Line : A line has only length. It has neither width nor thickness. 
 
(iii) Ray : It is a line (i.e. a straight line) that starts from a given fixed point and moves in 
the same direction. 
 
(iv) Line Segment: A line segmeftt is a part of a straight line. A line segment is a part of 
a line and also of a ray. 
 
(v) Surface : A surface has length and width, but no thickness. 
(vi) Plane : It is a flat surface. A plane has length and width, but no thickness. 
(vii) Parallel Lines : Two straight lines are said to be parallel to each other if they lie in 
the same plane and do not meet when produced on either side. 
 
(viii)Intersecting Lines : If two lines lie in the same plane and are not parallel to each 
other, they are called intersecting lines. 
(xi) Collinearity of Points : If three of more points lie on the same straight line, then 
the points are called collinear points. 
 
(x) Concurrent Lines : If three or more straight lines pass through the same point, the 
lines are called concurrent lines. 
 
EXERCISE 23 (A) 
Question 1. 
State, true or false, if false, correct the statement. 
(i) A dot has width but no length. 
(ii) A ray has an infinite length only on one side of it. 
(iii) A line segment PQ is written as  . 
(iv)   represents a straight line. 
(v) Three points are said to be collinear, if they lie in the same plane. 
(vi) Three or more points all lying in the same line, are called collinear points. 
Solution: 
(i) False : Because a dot has no length, no breadth. 
(ii) True. 
(iii) False : A line segment PQ is written as PQ. 
(iv) True. 
( v) False: Three points are called collinear points if they are in the same straight line. 
(vi) True. 
Question 2. 
Write how many lines can be drawn through : 
(i) a given point ? 
(ii) two given fixed points ? 
(iii) three collinear points ? 
(iv) three non-collinear points ? 
Solution: 
(i) Infinite (unlimited) line can be drawn through a given point. 
(ii) only one line can be drawn through two given point. 
(iii) only one line can be drawn through three collinear points. 
(iv) None (no) line can be drawn through three non-collinear points. 
Question 3. 
The shaded region of the given figure shows a plane : 
(a) Name : 
(i) three collinear points. 
(ii) three non-collinear points. 
(iii) a pair of intersecting lines. 
(b) State whether true or false : 
(i) Line DE is contained in the given plane P. 
(ii) Lines AB and DE intersect at point C. 
(iii) Points D, B and C are collinear. 
(iv) Points D, B and E are collinear. 
Solution: 
(a) (i) A, B and C are three collinear points. 
(ii) A, D and C are non-collinear points. 
(iii) AC and DE are intersecting lines. 
(b) (i) True 
(ii) True 
(iii) False 
(iv) False 
 
Question 4. 
Correct the statement, if it is wrong: 
(i) A A ray can be extended infinitely on either side. 
(ii) A ray has a definite length. 
(iii) A line segment has a definite length. 
(iv) A line has two end-points. 
(v) A ray has only one end point. 
Solution: 
(i) A ray can be extended infinitely on one side of it only. 
(ii) A ray has infinite length. 
(iii) Yes, a line segment has a definite length. 
(iv) A line-segment has two end-points. 
(v) Yes, a ray has only one end-point. 
Question 5. 
State true-er false, if false give the correct statement : 
(i) A line has a countable number of points in it. 
Page 4


IMPORTANT POINTS 
1. Fundamental Concepts : Geometry is the study of position,, shape, size and other 
properties of different figures. The geometrical terms such as : point, line, plane, etc., 
contain the basic ideas for the development of geometry. 
(i) Point : A point is a mark of position. It has neither length nor width nor. thickness and 
occupies no space. 
 
(ii) Line : A line has only length. It has neither width nor thickness. 
 
(iii) Ray : It is a line (i.e. a straight line) that starts from a given fixed point and moves in 
the same direction. 
 
(iv) Line Segment: A line segmeftt is a part of a straight line. A line segment is a part of 
a line and also of a ray. 
 
(v) Surface : A surface has length and width, but no thickness. 
(vi) Plane : It is a flat surface. A plane has length and width, but no thickness. 
(vii) Parallel Lines : Two straight lines are said to be parallel to each other if they lie in 
the same plane and do not meet when produced on either side. 
 
(viii)Intersecting Lines : If two lines lie in the same plane and are not parallel to each 
other, they are called intersecting lines. 
(xi) Collinearity of Points : If three of more points lie on the same straight line, then 
the points are called collinear points. 
 
(x) Concurrent Lines : If three or more straight lines pass through the same point, the 
lines are called concurrent lines. 
 
EXERCISE 23 (A) 
Question 1. 
State, true or false, if false, correct the statement. 
(i) A dot has width but no length. 
(ii) A ray has an infinite length only on one side of it. 
(iii) A line segment PQ is written as  . 
(iv)   represents a straight line. 
(v) Three points are said to be collinear, if they lie in the same plane. 
(vi) Three or more points all lying in the same line, are called collinear points. 
Solution: 
(i) False : Because a dot has no length, no breadth. 
(ii) True. 
(iii) False : A line segment PQ is written as PQ. 
(iv) True. 
( v) False: Three points are called collinear points if they are in the same straight line. 
(vi) True. 
Question 2. 
Write how many lines can be drawn through : 
(i) a given point ? 
(ii) two given fixed points ? 
(iii) three collinear points ? 
(iv) three non-collinear points ? 
Solution: 
(i) Infinite (unlimited) line can be drawn through a given point. 
(ii) only one line can be drawn through two given point. 
(iii) only one line can be drawn through three collinear points. 
(iv) None (no) line can be drawn through three non-collinear points. 
Question 3. 
The shaded region of the given figure shows a plane : 
(a) Name : 
(i) three collinear points. 
(ii) three non-collinear points. 
(iii) a pair of intersecting lines. 
(b) State whether true or false : 
(i) Line DE is contained in the given plane P. 
(ii) Lines AB and DE intersect at point C. 
(iii) Points D, B and C are collinear. 
(iv) Points D, B and E are collinear. 
Solution: 
(a) (i) A, B and C are three collinear points. 
(ii) A, D and C are non-collinear points. 
(iii) AC and DE are intersecting lines. 
(b) (i) True 
(ii) True 
(iii) False 
(iv) False 
 
Question 4. 
Correct the statement, if it is wrong: 
(i) A A ray can be extended infinitely on either side. 
(ii) A ray has a definite length. 
(iii) A line segment has a definite length. 
(iv) A line has two end-points. 
(v) A ray has only one end point. 
Solution: 
(i) A ray can be extended infinitely on one side of it only. 
(ii) A ray has infinite length. 
(iii) Yes, a line segment has a definite length. 
(iv) A line-segment has two end-points. 
(v) Yes, a ray has only one end-point. 
Question 5. 
State true-er false, if false give the correct statement : 
(i) A line has a countable number of points in it. 
(ii) Only one line can pass through a given point. 
(iii) The intersection of two planes is a straight line 
Solution: 
(i)  False, a line has length only. 
(ii) False, any number of line can pass through a given point. 
(iii) True. 
Question 6. 
State, whether the following pairs of lines or rays appear to be parallel or 
intersecting. 
 
 
Solution: 
(i) intersecting 
(ii) Parallel 
(iii) Parallel 
(iv) Intersecting 
Question 7. 
Give two examples, from your surroundings, for each of the following: 
(i) points 
(ii) line segments 
(iii) plane surfaces 
(iv) curved surfaces. 
Solution: 
Page 5


IMPORTANT POINTS 
1. Fundamental Concepts : Geometry is the study of position,, shape, size and other 
properties of different figures. The geometrical terms such as : point, line, plane, etc., 
contain the basic ideas for the development of geometry. 
(i) Point : A point is a mark of position. It has neither length nor width nor. thickness and 
occupies no space. 
 
(ii) Line : A line has only length. It has neither width nor thickness. 
 
(iii) Ray : It is a line (i.e. a straight line) that starts from a given fixed point and moves in 
the same direction. 
 
(iv) Line Segment: A line segmeftt is a part of a straight line. A line segment is a part of 
a line and also of a ray. 
 
(v) Surface : A surface has length and width, but no thickness. 
(vi) Plane : It is a flat surface. A plane has length and width, but no thickness. 
(vii) Parallel Lines : Two straight lines are said to be parallel to each other if they lie in 
the same plane and do not meet when produced on either side. 
 
(viii)Intersecting Lines : If two lines lie in the same plane and are not parallel to each 
other, they are called intersecting lines. 
(xi) Collinearity of Points : If three of more points lie on the same straight line, then 
the points are called collinear points. 
 
(x) Concurrent Lines : If three or more straight lines pass through the same point, the 
lines are called concurrent lines. 
 
EXERCISE 23 (A) 
Question 1. 
State, true or false, if false, correct the statement. 
(i) A dot has width but no length. 
(ii) A ray has an infinite length only on one side of it. 
(iii) A line segment PQ is written as  . 
(iv)   represents a straight line. 
(v) Three points are said to be collinear, if they lie in the same plane. 
(vi) Three or more points all lying in the same line, are called collinear points. 
Solution: 
(i) False : Because a dot has no length, no breadth. 
(ii) True. 
(iii) False : A line segment PQ is written as PQ. 
(iv) True. 
( v) False: Three points are called collinear points if they are in the same straight line. 
(vi) True. 
Question 2. 
Write how many lines can be drawn through : 
(i) a given point ? 
(ii) two given fixed points ? 
(iii) three collinear points ? 
(iv) three non-collinear points ? 
Solution: 
(i) Infinite (unlimited) line can be drawn through a given point. 
(ii) only one line can be drawn through two given point. 
(iii) only one line can be drawn through three collinear points. 
(iv) None (no) line can be drawn through three non-collinear points. 
Question 3. 
The shaded region of the given figure shows a plane : 
(a) Name : 
(i) three collinear points. 
(ii) three non-collinear points. 
(iii) a pair of intersecting lines. 
(b) State whether true or false : 
(i) Line DE is contained in the given plane P. 
(ii) Lines AB and DE intersect at point C. 
(iii) Points D, B and C are collinear. 
(iv) Points D, B and E are collinear. 
Solution: 
(a) (i) A, B and C are three collinear points. 
(ii) A, D and C are non-collinear points. 
(iii) AC and DE are intersecting lines. 
(b) (i) True 
(ii) True 
(iii) False 
(iv) False 
 
Question 4. 
Correct the statement, if it is wrong: 
(i) A A ray can be extended infinitely on either side. 
(ii) A ray has a definite length. 
(iii) A line segment has a definite length. 
(iv) A line has two end-points. 
(v) A ray has only one end point. 
Solution: 
(i) A ray can be extended infinitely on one side of it only. 
(ii) A ray has infinite length. 
(iii) Yes, a line segment has a definite length. 
(iv) A line-segment has two end-points. 
(v) Yes, a ray has only one end-point. 
Question 5. 
State true-er false, if false give the correct statement : 
(i) A line has a countable number of points in it. 
(ii) Only one line can pass through a given point. 
(iii) The intersection of two planes is a straight line 
Solution: 
(i)  False, a line has length only. 
(ii) False, any number of line can pass through a given point. 
(iii) True. 
Question 6. 
State, whether the following pairs of lines or rays appear to be parallel or 
intersecting. 
 
 
Solution: 
(i) intersecting 
(ii) Parallel 
(iii) Parallel 
(iv) Intersecting 
Question 7. 
Give two examples, from your surroundings, for each of the following: 
(i) points 
(ii) line segments 
(iii) plane surfaces 
(iv) curved surfaces. 
Solution: 
(i) Tips of your pencil (Ball Pen) and Tip of paper pin. 
(ii) Lines of Exercise Note-Books and edge of school desk. 
(iii) Floor of the room and top of the table. 
(iv) Surface of foot-ball and front glass of the car. 
Question 8. 
Under what condition will two straight 
lines, in the same plane, have : 
(i) no point in common. 
(ii) only one point in common. 
(iii) an infinite number of points in common. 
(iv) If possible draw diagrams in support of your answer. 
Solution: 
(i) When lines are parallel to each others. 
 
(ii) When they intersect each other 
 
Here, common point is E.