Page 1 Question:1 What is the difference between a theorem and an axiom? Solution: An axiom is a basic fact that is taken for granted without proof. Examples: i) Halves of equals are equal. ii) The whole is greater than each of its parts. Theorem: A statement that requires proof is called theorem. Examples: i) The sum of all the angles around a point is 360 ° . ii) The sum of all the angles of triangle is 180 ° . Question:2 Define the following terms: i Line segment ii Ray iii Intersecting lines iv Parallel lines v Half line vi Concurrent lines vii Collinear points viii Plane Solution: i Line segment :A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. i i Ray: A line with a start point but no end point and without a definite length is a ray. i i i Intersecting lines: Two lines with a common point are called intersecting lines. Page 2 Question:1 What is the difference between a theorem and an axiom? Solution: An axiom is a basic fact that is taken for granted without proof. Examples: i) Halves of equals are equal. ii) The whole is greater than each of its parts. Theorem: A statement that requires proof is called theorem. Examples: i) The sum of all the angles around a point is 360 ° . ii) The sum of all the angles of triangle is 180 ° . Question:2 Define the following terms: i Line segment ii Ray iii Intersecting lines iv Parallel lines v Half line vi Concurrent lines vii Collinear points viii Plane Solution: i Line segment :A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. i i Ray: A line with a start point but no end point and without a definite length is a ray. i i i Intersecting lines: Two lines with a common point are called intersecting lines. i v Parallel lines: Two lines in a plane without a common point are parallel lines. v Half line: A straight line extending from a point indefinitely in one direction only is a half line. v i Concurrent lines: Three or more lines intersecting at the same point are said to be concurrent. v i i Collinear points: Three or more than three points are said to be collinear if there is a line, which contains all the points. v i i i Plane: A plane is a surface such that every point of the line joining any two point on it, lies on it. Question:3 In the adjoining figure, name i six points ii five lines segments iii four rays iv four lines v four collinear points Solution: Page 3 Question:1 What is the difference between a theorem and an axiom? Solution: An axiom is a basic fact that is taken for granted without proof. Examples: i) Halves of equals are equal. ii) The whole is greater than each of its parts. Theorem: A statement that requires proof is called theorem. Examples: i) The sum of all the angles around a point is 360 ° . ii) The sum of all the angles of triangle is 180 ° . Question:2 Define the following terms: i Line segment ii Ray iii Intersecting lines iv Parallel lines v Half line vi Concurrent lines vii Collinear points viii Plane Solution: i Line segment :A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. i i Ray: A line with a start point but no end point and without a definite length is a ray. i i i Intersecting lines: Two lines with a common point are called intersecting lines. i v Parallel lines: Two lines in a plane without a common point are parallel lines. v Half line: A straight line extending from a point indefinitely in one direction only is a half line. v i Concurrent lines: Three or more lines intersecting at the same point are said to be concurrent. v i i Collinear points: Three or more than three points are said to be collinear if there is a line, which contains all the points. v i i i Plane: A plane is a surface such that every point of the line joining any two point on it, lies on it. Question:3 In the adjoining figure, name i six points ii five lines segments iii four rays iv four lines v four collinear points Solution: i Points are A, B, C, D, P and R. ii ¯ EF, ¯ GH, ¯ FH , ¯ EG, ¯ MN iii ? EP, ? GR, ? HS, ? FQ iv ? AB, ? CD, ? PQ, ? RS v Collinear points are M, E, G and B. Question:4 In the adjoining figure, name: i two pairs of intersecting lines and their corresponding points of intersection ii three concurrent lines and their points of intersection iii three rays iv two line segments Solution: i Two pairs of intersecting lines and their point of intersection are ? EF, ? GH, point R , ? AB, ? CD, point P ii Three concurrent lines are ? AB, ? EF, ? GH, point R iii Three rays are ? RB, ? RH, ? RF { } { } { } { } Page 4 Question:1 What is the difference between a theorem and an axiom? Solution: An axiom is a basic fact that is taken for granted without proof. Examples: i) Halves of equals are equal. ii) The whole is greater than each of its parts. Theorem: A statement that requires proof is called theorem. Examples: i) The sum of all the angles around a point is 360 ° . ii) The sum of all the angles of triangle is 180 ° . Question:2 Define the following terms: i Line segment ii Ray iii Intersecting lines iv Parallel lines v Half line vi Concurrent lines vii Collinear points viii Plane Solution: i Line segment :A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. i i Ray: A line with a start point but no end point and without a definite length is a ray. i i i Intersecting lines: Two lines with a common point are called intersecting lines. i v Parallel lines: Two lines in a plane without a common point are parallel lines. v Half line: A straight line extending from a point indefinitely in one direction only is a half line. v i Concurrent lines: Three or more lines intersecting at the same point are said to be concurrent. v i i Collinear points: Three or more than three points are said to be collinear if there is a line, which contains all the points. v i i i Plane: A plane is a surface such that every point of the line joining any two point on it, lies on it. Question:3 In the adjoining figure, name i six points ii five lines segments iii four rays iv four lines v four collinear points Solution: i Points are A, B, C, D, P and R. ii ¯ EF, ¯ GH, ¯ FH , ¯ EG, ¯ MN iii ? EP, ? GR, ? HS, ? FQ iv ? AB, ? CD, ? PQ, ? RS v Collinear points are M, E, G and B. Question:4 In the adjoining figure, name: i two pairs of intersecting lines and their corresponding points of intersection ii three concurrent lines and their points of intersection iii three rays iv two line segments Solution: i Two pairs of intersecting lines and their point of intersection are ? EF, ? GH, point R , ? AB, ? CD, point P ii Three concurrent lines are ? AB, ? EF, ? GH, point R iii Three rays are ? RB, ? RH, ? RF { } { } { } { } iv Two line segments are ¯ RQ and ¯ RP Question:5 From the given figure, name the following: a Three lines b One rectilinear figure c Four concurrent points Solution: a Line ? PQ , Line ? RS and Line ? AB b CEFG c No point is concurrent. Question:6 i How many lines can be drawn through a given point? ii How many lines can be drawn through two given points? iii At how many points can two lines at the most intersect? iv If A, B and C are three collinear points, name all the line segments determined by them. Solution: i Infinite lines can be drawn through a given point. { } Page 5 Question:1 What is the difference between a theorem and an axiom? Solution: An axiom is a basic fact that is taken for granted without proof. Examples: i) Halves of equals are equal. ii) The whole is greater than each of its parts. Theorem: A statement that requires proof is called theorem. Examples: i) The sum of all the angles around a point is 360 ° . ii) The sum of all the angles of triangle is 180 ° . Question:2 Define the following terms: i Line segment ii Ray iii Intersecting lines iv Parallel lines v Half line vi Concurrent lines vii Collinear points viii Plane Solution: i Line segment :A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. i i Ray: A line with a start point but no end point and without a definite length is a ray. i i i Intersecting lines: Two lines with a common point are called intersecting lines. i v Parallel lines: Two lines in a plane without a common point are parallel lines. v Half line: A straight line extending from a point indefinitely in one direction only is a half line. v i Concurrent lines: Three or more lines intersecting at the same point are said to be concurrent. v i i Collinear points: Three or more than three points are said to be collinear if there is a line, which contains all the points. v i i i Plane: A plane is a surface such that every point of the line joining any two point on it, lies on it. Question:3 In the adjoining figure, name i six points ii five lines segments iii four rays iv four lines v four collinear points Solution: i Points are A, B, C, D, P and R. ii ¯ EF, ¯ GH, ¯ FH , ¯ EG, ¯ MN iii ? EP, ? GR, ? HS, ? FQ iv ? AB, ? CD, ? PQ, ? RS v Collinear points are M, E, G and B. Question:4 In the adjoining figure, name: i two pairs of intersecting lines and their corresponding points of intersection ii three concurrent lines and their points of intersection iii three rays iv two line segments Solution: i Two pairs of intersecting lines and their point of intersection are ? EF, ? GH, point R , ? AB, ? CD, point P ii Three concurrent lines are ? AB, ? EF, ? GH, point R iii Three rays are ? RB, ? RH, ? RF { } { } { } { } iv Two line segments are ¯ RQ and ¯ RP Question:5 From the given figure, name the following: a Three lines b One rectilinear figure c Four concurrent points Solution: a Line ? PQ , Line ? RS and Line ? AB b CEFG c No point is concurrent. Question:6 i How many lines can be drawn through a given point? ii How many lines can be drawn through two given points? iii At how many points can two lines at the most intersect? iv If A, B and C are three collinear points, name all the line segments determined by them. Solution: i Infinite lines can be drawn through a given point. { } ii Only one line can be drawn through two given points. iii At most two lines can intersect at one point. iv The line segments determined by three collinear points A, B and C are AB, ¯ BC and AC. Question:7 Which of the following statements are true? i A line segment has no definite length. ii A ray has no end-point. iii A line has a definite length. iv A line ? AB is same as line ? BA . v A ray ? AB is same as ray ? BA . vi Two distinct points always determine a unique line. vii Three lines are concurrent if they have a common point. viii Two distinct lines cannot have more than one point in common. ix Two intersecting lines cannot be both parallel to the same line. x Open half-line is the same thing as ray. xi Two lines may intersect in two points. xii Two lines are parallel only when they have no point in common. Solution: i False. A line segment has a definite length. ii False. A ray has one end-point.Read More

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