Class 7 Notes - Lines and Angles

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Lines and Angles

In this chapter, students will deepen their understanding of lines and angles, their types, properties, and how they relate to each other. This knowledge is foundational for geometry and higher mathematics.

1. Basic Terms and Definitions

  • Line: A straight path that extends endlessly in both directions.
  • Line Segment: A part of a line with two endpoints.
  • Ray: A part of a line that starts at one point and extends endlessly in one direction.
  • Collinear Points: Points that lie on the same straight line.
  • Intersecting Lines: Lines that cross each other at a point.
  • Parallel Lines: Lines in a plane that never meet, no matter how far they are extended.
  • Transversal: A line that crosses two or more lines at distinct points.

2. Types of Angles

  • Acute Angle: Less than 90°
  • Right Angle: Exactly 90°
  • Obtuse Angle: Greater than 90° but less than 180°
  • Straight Angle: Exactly 180°
  • Reflex Angle: Greater than 180° but less than 360°
  • Complete Angle: Exactly 360°

3. Pairs of Angles

  • Complementary Angles: Two angles whose sum is 90°
  • Supplementary Angles: Two angles whose sum is 180°
  • Adjacent Angles: Angles that have a common vertex and a common arm but do not overlap
  • Linear Pair: A pair of adjacent angles whose non-common arms form a straight line (sum is 180°)
  • Vertically Opposite Angles: Angles opposite each other when two lines cross; they are always equal

4. Properties and Theorems

  • Vertically opposite angles are equal.
  • The sum of angles on a straight line is 180°.
  • The sum of angles around a point is 360°.
  • If two lines are parallel and are cut by a transversal, then:
    • Corresponding angles are equal.
    • Alternate interior angles are equal.
    • Co-interior (consecutive) angles are supplementary.

5. Real-Life Examples

  • Railway tracks (parallel lines)
  • Scissors (intersecting lines)
  • Clock hands (angles)
  • Road crossings (transversals and angles)

6. Practice Questions

  1. Draw and label a line, a line segment, and a ray.
  2. Classify the following angles: 45°, 90°, 120°, 180°, 270°, 360°.
  3. If two angles are supplementary and one is 110°, what is the other?
  4. Find the value of x if two vertically opposite angles are (3x + 10)° and (5x – 30)°.
  5. In the figure, if lines AB and CD are parallel and EF is a transversal, identify all pairs of corresponding angles.

7. Summary

  • Lines can be straight, parallel, or intersecting.
  • Angles are classified based on their measure.
  • Pairs of angles have special properties.
  • Understanding lines and angles is essential for geometry and real-life applications.