Class 6 Maths Lines and Angles Notes

Class 6 Maths Lines and Angles Notes

1. Introduction

  • Line: A straight path that extends infinitely in both directions.
  • Line Segment: A part of a line with two endpoints.
  • Ray: A part of a line with one endpoint and extends infinitely in one direction.

2. Types of Lines

  1. Parallel Lines:
    • Lines that never meet, no matter how far they are extended.
    • Example: Railway tracks, opposite sides of a rectangle.
  2. Intersecting Lines:
    • Lines that meet or cross each other at a point.
  3. Perpendicular Lines:
    • Lines that intersect at a 90° angle.

3. Angles

  • Angle: Formed when two rays meet at a common endpoint called the vertex.
  • Vertex: The point where two rays meet.
  • Arm of an Angle: Each ray forming the angle.

Types of Angles

  1. Acute Angle: Less than 90°
  2. Right Angle: Exactly 90°
  3. Obtuse Angle: Greater than 90° but less than 180°
  4. Straight Angle: Exactly 180°
  5. Reflex Angle: Greater than 180°

4. Adjacent and Linear Pair of Angles

  • Adjacent Angles: Two angles with a common vertex and a common arm, without overlapping.
  • Linear Pair: Two adjacent angles whose sum is 180°.

5. Angles on a Straight Line and at a Point

  • Angles on a Straight Line: The sum of angles on a straight line is 180°.
  • Angles at a Point: The sum of angles around a point is 360°.

6. Vertically Opposite Angles

  • When two lines intersect, opposite angles are equal.

7. Properties of Parallel Lines

  • If a transversal intersects two parallel lines, it forms:
    1. Corresponding Angles – Equal
    2. Alternate Interior Angles – Equal
    3. Alternate Exterior Angles – Equal
    4. Co-Interior (Consecutive Interior) Angles – Sum = 180°

8. Practice Examples

  1. Identify the type of angle: 75°, 120°, 180°, 95°
  2. Draw a pair of perpendicular lines.
  3. Find the missing angle if one angle is 65° and it forms a linear pair.
  4. Identify corresponding and alternate angles in parallel lines with a transversal.

Questions

Part A – Multiple Choice Questions (MCQs) – 20 Questions

  1. A line segment has
    a) Two endpoints
    b) No endpoints
    c) One endpoint
    d) Three endpoints
  2. A ray has
    a) Two endpoints
    b) One endpoint and extends infinitely in one direction
    c) No endpoints
    d) Infinite endpoints
  3. Two lines that never meet are called
    a) Intersecting lines
    b) Parallel lines
    c) Perpendicular lines
    d) Curved lines
  4. The angle formed by perpendicular lines is
    a) 45°
    b) 90°
    c) 180°
    d) 60°
  5. The sum of angles on a straight line is
    a) 90°
    b) 180°
    c) 360°
    d) 270°
  6. Vertically opposite angles are
    a) Equal
    b) Supplementary
    c) Complementary
    d) None of these
  7. The sum of angles at a point is
    a) 90°
    b) 180°
    c) 360°
    d) 270°
  8. An obtuse angle is
    a) Less than 90°
    b) Exactly 90°
    c) More than 90° but less than 180°
    d) More than 180°
  9. A reflex angle is
    a) Less than 90°
    b) Between 90° and 180°
    c) Greater than 180°
    d) 90°
  10. Two adjacent angles forming a straight line are called
    a) Vertical angles
    b) Linear pair
    c) Reflex angles
    d) Complementary angles
  11. Alternate interior angles are
    a) Equal
    b) Supplementary
    c) Right angles
    d) Obtuse
  12. Corresponding angles are formed when a ___ intersects two parallel lines.
    a) Line
    b) Transversal
    c) Curve
    d) Ray
  13. Two perpendicular lines meet at
    a) 45°
    b) 90°
    c) 120°
    d) 180°
  14. The sum of two angles forming a linear pair is
    a) 90°
    b) 180°
    c) 360°
    d) 270°
  15. Angles less than 90° are called
    a) Acute angles
    b) Obtuse angles
    c) Right angles
    d) Straight angles
  16. The angle of a straight line is
    a) 90°
    b) 180°
    c) 360°
    d) 270°
  17. The sum of interior angles on the same side of a transversal intersecting two parallel lines is
    a) 90°
    b) 180°
    c) 360°
    d) 270°
  18. Lines that intersect at 90° are called
    a) Parallel
    b) Perpendicular
    c) Intersecting
    d) Non-intersecting
  19. Two angles on opposite sides of an intersecting point are called
    a) Adjacent angles
    b) Linear pair
    c) Vertically opposite angles
    d) Corresponding angles
  20. An angle equal to 180° is
    a) Right angle
    b) Straight angle
    c) Reflex angle
    d) Acute angle

Part B – Fill in the Blanks – 20 Questions

  1. The point where two lines meet is called __________.
  2. A line extending infinitely in both directions is called __________.
  3. Two lines that never meet are called __________.
  4. An angle equal to 90° is called __________.
  5. Two adjacent angles whose sum is 180° are called __________.
  6. The sum of angles around a point is __________.
  7. Two angles opposite to each other when two lines intersect are __________.
  8. Angles less than 90° are __________ angles.
  9. An angle more than 180° is called a __________ angle.
  10. The sum of angles on a straight line is __________.
  11. Lines intersecting at 90° are called __________ lines.
  12. Angles on the same side of a transversal are __________.
  13. Corresponding angles are formed when a __________ intersects two parallel lines.
  14. A part of a line with two endpoints is called a __________.
  15. A part of a line with one endpoint is called a __________.
  16. Vertical angles are always __________.
  17. Alternate interior angles are __________.
  18. The sum of two angles in a linear pair is __________.
  19. A straight angle measures __________.
  20. An obtuse angle is __________ than 90° but less than 180°.

Part C – True/False – 10 Questions

  1. Two intersecting lines always form right angles.
  2. Vertically opposite angles are equal.
  3. Parallel lines intersect at some point.
  4. The sum of angles at a point is 360°.
  5. A straight angle is equal to 180°.
  6. Adjacent angles share a common arm.
  7. Reflex angles are less than 180°.
  8. Alternate exterior angles are equal if lines are parallel.
  9. Lines perpendicular to each other form 45° angles.
  10. A line segment has infinite length

Part D – Match the Following – 10 Questions

Column AColumn B
51. Acute anglea) 180°
52. Right angleb) < 90°
53. Obtuse anglec) > 90° but < 180°
54. Straight angled) 90°
55. Reflex anglee) > 180°
56. Parallel linesf) Never meet
57. Perpendicular linesg) Meet at 90°
58. Adjacent anglesh) Share a common arm and vertex
59. Linear pairi) Sum = 180°
60. Sum of angles at a pointj) 360°

Part E – Short Answer/Problem Solving – 40 Questions

  1. Draw two parallel lines and a transversal. Label corresponding angles.
  2. Draw two perpendicular lines and measure the angles formed.
  3. If one angle of a linear pair is 65°, find the other.
  4. Find the missing angle if vertically opposite angle = 110°.
  5. Draw an acute, obtuse, and right angle.
  6. A reflex angle measures 250°. Find its corresponding acute angle.
  7. Draw a straight angle using a protractor.
  8. Draw two intersecting lines and label all vertically opposite angles.
  9. Identify alternate interior angles in a given figure.
  10. Identify alternate exterior angles in a given figure.
  11. If ∠A + ∠B = 180°, find ∠B when ∠A = 120°.
  12. Draw a line segment of 5 cm.
  13. Draw a ray starting from a given point.
  14. Draw a line that is perpendicular to a given line.
  15. Draw a pair of adjacent angles.
  16. Find the missing angle in a linear pair if one angle = 135°.
  17. Draw a straight line and mark two points on it.
  18. Draw two parallel lines and show co-interior angles.
  19. Draw an obtuse angle of 120°.
  20. Draw an acute angle of 45°.
  21. Measure a 90° angle using a protractor.
  22. Draw an angle of 150° (obtuse).
  23. Draw a reflex angle of 210°.
  24. Draw two intersecting lines and label the angles formed.
  25. Identify corresponding angles in a diagram with parallel lines.
  26. Identify a linear pair in a given figure.
  27. Find the sum of angles on a straight line if one angle = 70°.
  28. Find the sum of angles around a point if three angles are 100°, 120°, 50°.
  29. Draw a triangle and mark all interior angles.
  30. Identify adjacent angles in a given figure.
  31. Draw two parallel lines and a transversal. Identify alternate interior and exterior angles.
  32. Draw perpendicular lines intersecting at a point. Measure the angles.
  33. Find the missing angle in a vertically opposite angle if one angle = 75°.
  34. Draw a pair of supplementary angles.
  35. Draw a line segment of 6 cm and a ray starting from one endpoint.
  36. Draw an angle of 135° (obtuse

Answers

  1. a) Two endpoints
  2. b) One endpoint and extends infinitely in one direction
  3. b) Parallel lines
  4. b) 90°
  5. b) 180°
  6. a) Equal
  7. c) 360°
  8. c) More than 90° but less than 180°
  9. c) Greater than 180°
  10. b) Linear pair
  11. a) Equal
  12. b) Transversal
  13. b) 90°
  14. b) 180°
  15. a) Acute angles
  16. b) 180°
  17. b) 180°
  18. b) Perpendicular
  19. c) Vertically opposite angles
  20. b) Straight angle

Part B – Fill in the Blanks (Answers)

  1. Vertex
  2. Line
  3. Parallel lines
  4. Right angle
  5. Linear pair
  6. 360°
  7. Vertically opposite angles
  8. Acute
  9. Reflex
  10. 180°
  11. Perpendicular
  12. Supplementary (or Co-interior)
  13. Transversal
  14. Line segment
  15. Ray
  16. Equal
  17. Equal
  18. 180°
  19. 180°
  20. Greater

Part C – True/False (Answers)

  1. False
  2. True
  3. False
  4. True
  5. True
  6. True
  7. False
  8. True
  9. False
  10. False

Part D – Match the Following (Answers)

51 → b) < 90°
52 → d) 90°
53 → c) > 90° < 180°
54 → a) 180°
55 → e) > 180°
56 → f) Never meet
57 → g) Meet at 90°
58 → h) Share a common arm and vertex
59 → i) Sum = 180°
60 → j) 360°

Part E – Short Answer/Problem Solving (Solutions)

  1. Draw two parallel lines and a transversal; mark equal corresponding angles on same side.
  2. Draw two perpendicular lines intersecting; each angle = 90°.
  3. Other angle = 180° – 65° = 115°
  4. Vertically opposite angle = 110° → other opposite angle also 110°
  5. Draw examples: Acute < 90°, Right = 90°, Obtuse > 90°
  6. Reflex angle = 250° → corresponding acute angle = 360° – 250° = 110°
  7. Draw a straight line; mark angle along the line = 180°
  8. Label vertically opposite angles as equal pairs
  9. Identify angles between parallel lines on alternate interior sides of transversal
  10. Identify angles outside parallel lines on opposite sides of transversal
  11. ∠B = 180° – 120° = 60°
  12. Draw a straight line segment 5 cm using a ruler
  13. Draw a ray starting from a point; one endpoint, extends infinitely in one direction
  14. Draw perpendicular from a point on the line; use 90°
  15. Draw two angles sharing a common vertex and arm
  16. Missing angle = 180° – 135° = 45°
  17. Draw a straight line and mark two points anywhere
  18. Draw two parallel lines; label interior angles on same side of transversal; sum = 180°
  19. Draw obtuse angle 120°
  20. Draw acute angle 45°
  21. Measure right angle 90° with protractor
  22. Draw obtuse angle 150°
  23. Draw reflex angle 210°
  24. Draw intersecting lines; label opposite angles as equal
  25. Identify angles in same relative positions to parallel lines → corresponding angles equal
  26. Identify adjacent angles whose sum = 180°
  27. Missing angle = 180° – 70° = 110°
  28. Sum = 360° – (100 + 120 + 50) = 90° remaining angle
  29. Draw triangle; label three interior angles; sum = 180°
  30. Identify angles sharing a common arm and vertex
  31. Draw transversal intersecting parallel lines; label alternate interior and exterior angles
  32. Draw perpendicular lines intersecting; each angle = 90°
  33. Vertically opposite angle = 75° → opposite angle = 75°
  34. Draw supplementary angles → sum = 180°
  35. Draw line segment 6 cm; ray from endpoint extends infinitely
  36. Draw obtuse angle 135°
  37. Draw acute angle 60°
  38. Draw two parallel lines; transversal intersects; label co-interior angles → sum = 180°
  39. Draw intersecting lines; measure all angles; verify vertically opposite angles equal
  40. Draw two parallel lines; transversal intersects; identify corresponding, alternate interior, alternate exterior, and co-interior angles