Page 1 EXERCISE 11 (A) Q.1. Name all the line segments in each of the following figures : Y Z X A C B D E (i) (ii) P Q R S (iii) Sol. Line segment (i) In figure (i) are XY and YZ (ii) In figure (ii) AD , AB , AC, AE , BD , BC , CE (iii) In figure (iii) PQ , PR , PS , QR , QS and RS Q. 2. Identify and name the line segments and rays in each of the following figures : Sol. (i) In fig. (i), line segments is AB, and rays are AC and BD . (ii) In fig. (ii), line segments are GE GP EP , , and rays are EF GH PQ , , . (iii) In fig. (iii), line segments are OL OP , and rays are LM PQ , . Q. 3. In the adjoining figure, name (i) four line segments ; (ii) four rays ; (iii) two non-intersecting line segments. Sol. (i) Four line segments are PR QR PQ , , and RS. (ii) Four ray can be PA QC RB SD , , , (iii) PR and QS are two non-intersecting lines. Q. 4. What do you mean by collinear points ? Page 2 EXERCISE 11 (A) Q.1. Name all the line segments in each of the following figures : Y Z X A C B D E (i) (ii) P Q R S (iii) Sol. Line segment (i) In figure (i) are XY and YZ (ii) In figure (ii) AD , AB , AC, AE , BD , BC , CE (iii) In figure (iii) PQ , PR , PS , QR , QS and RS Q. 2. Identify and name the line segments and rays in each of the following figures : Sol. (i) In fig. (i), line segments is AB, and rays are AC and BD . (ii) In fig. (ii), line segments are GE GP EP , , and rays are EF GH PQ , , . (iii) In fig. (iii), line segments are OL OP , and rays are LM PQ , . Q. 3. In the adjoining figure, name (i) four line segments ; (ii) four rays ; (iii) two non-intersecting line segments. Sol. (i) Four line segments are PR QR PQ , , and RS. (ii) Four ray can be PA QC RB SD , , , (iii) PR and QS are two non-intersecting lines. Q. 4. What do you mean by collinear points ? (i) How many lines can you draw passing through three collinear points ? (ii) Given three collinear points A, B, C. How many lines segments do they determine ? Name them. Sol. (i) Three or more points in a plane are said to be collinear if they all lie on the same line. (ii) In the figure given above, points A, B, C are collinear points. We can draw exactly one line passing through three collinear points. Q. 5. In the adjoining figure name : (i) Four pairs of intersectong lines. (ii) Four collinear points (iii) Three non-collinear points (iv) Three concurrent lines (v) Three lines whose point of intersection is P. Sol. (i) Four pairs of intersecting lines are : (AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS) (ii) Four collinear points are : A, Q, S, B (iii) Three non-collinear points are : A, Q, P (iv) Three concurrent lines are : AB, PS and RS. (v) Three lines whose point of intersecton is P are : CD, PQ and PS. Q. 6. Mark three non-collinear points A, B, C as shown. Draw lines through these points taking two at a time. Name the lines. How many such different lines can be drawn. Sol. The lines drawn through given points A, B, C are as shown below. The names of these lines are AB, BC and AC. A B C Also it is clear that three different lines can be drawn. Q. 7. Count the number of line segments in each of the following figures and name them : C Page 3 EXERCISE 11 (A) Q.1. Name all the line segments in each of the following figures : Y Z X A C B D E (i) (ii) P Q R S (iii) Sol. Line segment (i) In figure (i) are XY and YZ (ii) In figure (ii) AD , AB , AC, AE , BD , BC , CE (iii) In figure (iii) PQ , PR , PS , QR , QS and RS Q. 2. Identify and name the line segments and rays in each of the following figures : Sol. (i) In fig. (i), line segments is AB, and rays are AC and BD . (ii) In fig. (ii), line segments are GE GP EP , , and rays are EF GH PQ , , . (iii) In fig. (iii), line segments are OL OP , and rays are LM PQ , . Q. 3. In the adjoining figure, name (i) four line segments ; (ii) four rays ; (iii) two non-intersecting line segments. Sol. (i) Four line segments are PR QR PQ , , and RS. (ii) Four ray can be PA QC RB SD , , , (iii) PR and QS are two non-intersecting lines. Q. 4. What do you mean by collinear points ? (i) How many lines can you draw passing through three collinear points ? (ii) Given three collinear points A, B, C. How many lines segments do they determine ? Name them. Sol. (i) Three or more points in a plane are said to be collinear if they all lie on the same line. (ii) In the figure given above, points A, B, C are collinear points. We can draw exactly one line passing through three collinear points. Q. 5. In the adjoining figure name : (i) Four pairs of intersectong lines. (ii) Four collinear points (iii) Three non-collinear points (iv) Three concurrent lines (v) Three lines whose point of intersection is P. Sol. (i) Four pairs of intersecting lines are : (AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS) (ii) Four collinear points are : A, Q, S, B (iii) Three non-collinear points are : A, Q, P (iv) Three concurrent lines are : AB, PS and RS. (v) Three lines whose point of intersecton is P are : CD, PQ and PS. Q. 6. Mark three non-collinear points A, B, C as shown. Draw lines through these points taking two at a time. Name the lines. How many such different lines can be drawn. Sol. The lines drawn through given points A, B, C are as shown below. The names of these lines are AB, BC and AC. A B C Also it is clear that three different lines can be drawn. Q. 7. Count the number of line segments in each of the following figures and name them : C Sol. (i) In the the given figure, there are six line segments, namely AB, AC, AD, BD, BC, DC. (ii) In the given figure, there are ten line segments, namely, AD, AB, AC, AO, OC, BC, BD, BO, OD, CD. (iii) In the given figure, there are six line segments, namely AB, AF, BF, CD, DE, CE. (iv) In the given figure, there are twelve line segments, namely, AB, BC, CD, AD, BF, CG, DH, AE, EF, FG, GH, EH. Q.8. Consider the line PQ given below and find whether the given statements are true or false : P L M N Q (i) M is a point on ray NQ . (ii) L is a point on ray MP . (iii) Ray MQ is different from ray NQ . (iv) L, M, N are points on line segment LN . (v) Ray LP is different from ray LQ . Sol. PQ is a line P L M N Q (i) False, as M does not lie on NQ (ii) True (iii) True (iv) True (v) True Q. 9. 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 AB is the same as the ray BA . (v) The line segment AB is the same as the line segment BA. (vi) The line AB is the same as the line 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 Page 4 EXERCISE 11 (A) Q.1. Name all the line segments in each of the following figures : Y Z X A C B D E (i) (ii) P Q R S (iii) Sol. Line segment (i) In figure (i) are XY and YZ (ii) In figure (ii) AD , AB , AC, AE , BD , BC , CE (iii) In figure (iii) PQ , PR , PS , QR , QS and RS Q. 2. Identify and name the line segments and rays in each of the following figures : Sol. (i) In fig. (i), line segments is AB, and rays are AC and BD . (ii) In fig. (ii), line segments are GE GP EP , , and rays are EF GH PQ , , . (iii) In fig. (iii), line segments are OL OP , and rays are LM PQ , . Q. 3. In the adjoining figure, name (i) four line segments ; (ii) four rays ; (iii) two non-intersecting line segments. Sol. (i) Four line segments are PR QR PQ , , and RS. (ii) Four ray can be PA QC RB SD , , , (iii) PR and QS are two non-intersecting lines. Q. 4. What do you mean by collinear points ? (i) How many lines can you draw passing through three collinear points ? (ii) Given three collinear points A, B, C. How many lines segments do they determine ? Name them. Sol. (i) Three or more points in a plane are said to be collinear if they all lie on the same line. (ii) In the figure given above, points A, B, C are collinear points. We can draw exactly one line passing through three collinear points. Q. 5. In the adjoining figure name : (i) Four pairs of intersectong lines. (ii) Four collinear points (iii) Three non-collinear points (iv) Three concurrent lines (v) Three lines whose point of intersection is P. Sol. (i) Four pairs of intersecting lines are : (AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS) (ii) Four collinear points are : A, Q, S, B (iii) Three non-collinear points are : A, Q, P (iv) Three concurrent lines are : AB, PS and RS. (v) Three lines whose point of intersecton is P are : CD, PQ and PS. Q. 6. Mark three non-collinear points A, B, C as shown. Draw lines through these points taking two at a time. Name the lines. How many such different lines can be drawn. Sol. The lines drawn through given points A, B, C are as shown below. The names of these lines are AB, BC and AC. A B C Also it is clear that three different lines can be drawn. Q. 7. Count the number of line segments in each of the following figures and name them : C Sol. (i) In the the given figure, there are six line segments, namely AB, AC, AD, BD, BC, DC. (ii) In the given figure, there are ten line segments, namely, AD, AB, AC, AO, OC, BC, BD, BO, OD, CD. (iii) In the given figure, there are six line segments, namely AB, AF, BF, CD, DE, CE. (iv) In the given figure, there are twelve line segments, namely, AB, BC, CD, AD, BF, CG, DH, AE, EF, FG, GH, EH. Q.8. Consider the line PQ given below and find whether the given statements are true or false : P L M N Q (i) M is a point on ray NQ . (ii) L is a point on ray MP . (iii) Ray MQ is different from ray NQ . (iv) L, M, N are points on line segment LN . (v) Ray LP is different from ray LQ . Sol. PQ is a line P L M N Q (i) False, as M does not lie on NQ (ii) True (iii) True (iv) True (v) True Q. 9. 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 AB is the same as the ray BA . (v) The line segment AB is the same as the line segment BA. (vi) The line AB is the same as the line 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 collinear then the points 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. Sol. (i) False . . . Point has no dimensions. (ii) False . . . A line segment has a length. (iii) False . . . A ray has no finite length. (iv) False . . . If AB and ray BA have opposite directions. (v) True . . . Length of AB and BA is same. (vi) True . . . Line AB and BA are same. (vii) True . . . Distance between A and B or B and A is same, so they determine a unique line segment. (viii) True . . . Two lines intersect each other at one point. (ix) False . . . Two intersecting planes intersect at one line not at one point. (x) False . . . If A, B, C are collinear and points C, D, E are collinear then it is not necessary that there points A, B, C, D and E are collinear. (xi) False . . . Infinite number of rays can be drawn with a given end point. (xii) True . . . We can draw one and only one line passing through two given points. (xiii) True . . . We can draw infinite number of lines pass through a given point. Q. 10. Fill in the blanks : (i) A line segment has a ............ length. (ii) A ray has ............ end point. (iii) A line has ............ end point. (iv) A ray has no ............ length. (v) A line ............ be drawn on a paper. Sol. (i) definite (ii) one (iii) no (iv) definite (v) cannot. Ans. EXERCISE 11 (B) Mark ( ) against the correct answer in each of following. Q. 1. Which of the following has no end points ? (a) a line segment (b) a ray (c) a line (d) none of these Sol. (c) a line has no end points Q. 2. Which of the following has one end point ? (a) a line (b) a ray (c) a line segment (d) none of these Sol. (b) a ray has no end points Q. 3. Which of the following has two end points ? (a) a line segment (b) a ray (c) a line (d) none of these Sol. (a) a line segment has two end points Q. 4. Which of the following has definite length ? (a) a line (b) a line segment (c) a ray (d) none of these Sol. (b) a line segment has definite length Q. 5. Which of the following can be drawn on a piece of paper ? (a) a line (b) a line segment (c) a ray (d) a plane Sol. (b) a line segment can be drawn on a piece of paper Q. 6. How many lines can be drawn passing through a given point ? Page 5 EXERCISE 11 (A) Q.1. Name all the line segments in each of the following figures : Y Z X A C B D E (i) (ii) P Q R S (iii) Sol. Line segment (i) In figure (i) are XY and YZ (ii) In figure (ii) AD , AB , AC, AE , BD , BC , CE (iii) In figure (iii) PQ , PR , PS , QR , QS and RS Q. 2. Identify and name the line segments and rays in each of the following figures : Sol. (i) In fig. (i), line segments is AB, and rays are AC and BD . (ii) In fig. (ii), line segments are GE GP EP , , and rays are EF GH PQ , , . (iii) In fig. (iii), line segments are OL OP , and rays are LM PQ , . Q. 3. In the adjoining figure, name (i) four line segments ; (ii) four rays ; (iii) two non-intersecting line segments. Sol. (i) Four line segments are PR QR PQ , , and RS. (ii) Four ray can be PA QC RB SD , , , (iii) PR and QS are two non-intersecting lines. Q. 4. What do you mean by collinear points ? (i) How many lines can you draw passing through three collinear points ? (ii) Given three collinear points A, B, C. How many lines segments do they determine ? Name them. Sol. (i) Three or more points in a plane are said to be collinear if they all lie on the same line. (ii) In the figure given above, points A, B, C are collinear points. We can draw exactly one line passing through three collinear points. Q. 5. In the adjoining figure name : (i) Four pairs of intersectong lines. (ii) Four collinear points (iii) Three non-collinear points (iv) Three concurrent lines (v) Three lines whose point of intersection is P. Sol. (i) Four pairs of intersecting lines are : (AB, PQ) ; (AB, RS) ; (CD, PQ) ; (CD, RS) (ii) Four collinear points are : A, Q, S, B (iii) Three non-collinear points are : A, Q, P (iv) Three concurrent lines are : AB, PS and RS. (v) Three lines whose point of intersecton is P are : CD, PQ and PS. Q. 6. Mark three non-collinear points A, B, C as shown. Draw lines through these points taking two at a time. Name the lines. How many such different lines can be drawn. Sol. The lines drawn through given points A, B, C are as shown below. The names of these lines are AB, BC and AC. A B C Also it is clear that three different lines can be drawn. Q. 7. Count the number of line segments in each of the following figures and name them : C Sol. (i) In the the given figure, there are six line segments, namely AB, AC, AD, BD, BC, DC. (ii) In the given figure, there are ten line segments, namely, AD, AB, AC, AO, OC, BC, BD, BO, OD, CD. (iii) In the given figure, there are six line segments, namely AB, AF, BF, CD, DE, CE. (iv) In the given figure, there are twelve line segments, namely, AB, BC, CD, AD, BF, CG, DH, AE, EF, FG, GH, EH. Q.8. Consider the line PQ given below and find whether the given statements are true or false : P L M N Q (i) M is a point on ray NQ . (ii) L is a point on ray MP . (iii) Ray MQ is different from ray NQ . (iv) L, M, N are points on line segment LN . (v) Ray LP is different from ray LQ . Sol. PQ is a line P L M N Q (i) False, as M does not lie on NQ (ii) True (iii) True (iv) True (v) True Q. 9. 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 AB is the same as the ray BA . (v) The line segment AB is the same as the line segment BA. (vi) The line AB is the same as the line 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 collinear then the points 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. Sol. (i) False . . . Point has no dimensions. (ii) False . . . A line segment has a length. (iii) False . . . A ray has no finite length. (iv) False . . . If AB and ray BA have opposite directions. (v) True . . . Length of AB and BA is same. (vi) True . . . Line AB and BA are same. (vii) True . . . Distance between A and B or B and A is same, so they determine a unique line segment. (viii) True . . . Two lines intersect each other at one point. (ix) False . . . Two intersecting planes intersect at one line not at one point. (x) False . . . If A, B, C are collinear and points C, D, E are collinear then it is not necessary that there points A, B, C, D and E are collinear. (xi) False . . . Infinite number of rays can be drawn with a given end point. (xii) True . . . We can draw one and only one line passing through two given points. (xiii) True . . . We can draw infinite number of lines pass through a given point. Q. 10. Fill in the blanks : (i) A line segment has a ............ length. (ii) A ray has ............ end point. (iii) A line has ............ end point. (iv) A ray has no ............ length. (v) A line ............ be drawn on a paper. Sol. (i) definite (ii) one (iii) no (iv) definite (v) cannot. Ans. EXERCISE 11 (B) Mark ( ) against the correct answer in each of following. Q. 1. Which of the following has no end points ? (a) a line segment (b) a ray (c) a line (d) none of these Sol. (c) a line has no end points Q. 2. Which of the following has one end point ? (a) a line (b) a ray (c) a line segment (d) none of these Sol. (b) a ray has no end points Q. 3. Which of the following has two end points ? (a) a line segment (b) a ray (c) a line (d) none of these Sol. (a) a line segment has two end points Q. 4. Which of the following has definite length ? (a) a line (b) a line segment (c) a ray (d) none of these Sol. (b) a line segment has definite length Q. 5. Which of the following can be drawn on a piece of paper ? (a) a line (b) a line segment (c) a ray (d) a plane Sol. (b) a line segment can be drawn on a piece of paper Q. 6. How many lines can be drawn passing through a given point ? (a) one only (b) two (c) three (d) unlimited number Sol. (d) unlimited number can be drawn passing through a given point Q. 7. How many lines can be drawn passing through two given points ? (a) one only (b) two (c) three (d) unlimited number Sol. (a) one only can be drawn passing through two given points 1. (c) . . . A line has no end points. 2. (b) . . . A ray his one end point. 3. (a) . . . A line segment has two end points. 4. (b) . . . A line segment has definite length. 5. (b) . . . A line segment can be drawn on a piece of paper. 6. (d) . . . Unlimited number of lines can be draw passing through a given point. 7. (a) . . . One and only one line can be drawn passing through two given points. Q.8. Two planes intersect (a) at a point (b) in a plane (c) in a line (d) none of these Sol. Two planes intersect in a line. (c) Q.9. Two lines intersect (a) at a point (b) at two points (c) at an infinite number of points (d) in a line Sol. Two lines intersect at a point. (a) Q.10. Two points in a plane determine (a) exactly one line segment (b) exactly two line segments (c) an infinite number of line segments (d) none of these Sol. Two points in a plane determine exactly one line segment. (a) Q.11. The minimum number of points of intersection of three lines in a plane is (a) 1 (b) 2 (c) 3 (d) 0 Sol. The minimum number of points of intersection of three lines in a plane is 0. (d) Q.12. The maximum number of points of intersection of three lines in a plane is (a) 0 (b) 1 (c) 2 (d) 3 Sol. The maximum number of a points of intersection of three lines in a plane is 3 (d) Q.13. Choose the correct statement : (a) every line has a definite length (b) every ray has a definite length (c) every line segment has a definite length (d) none of these Sol. Every line segment has a definite length. (c) Q.14. Choose the false statement : (a) Line AB is the same as line BA (b) Ray AB is the same as ray BA (c) Line segment AB is the same as the line segment BA (d) none of these Sol. Ray AB is not same as ray BA Both are different. Hence AB is same as BA is false. (b) Q.15. How many rays can be drawn with a given point as the initial point ? (a) One (b) Two (c) An unlimited number (d) A limited number only Sol. An unlimited number of rays can be drawn with a given point as the initial point. 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