Understanding Lines and Angles

Jul 13, 2024

Lines and Angles (Chapter 5 - Class 7 NCERT)

Lines

  • When a dot on a plane is extended in one direction without lifting the pen, it is called a line.
  • Line Segment - It has two endpoints.
  • Ray - It has one endpoint and extends infinitely in the other direction.
  • Line - It has no endpoints and extends infinitely in both directions.

Angles

  • When two or more lines meet at a point, angles are formed at that point.
  • In the nomenclature of angles, the central point is considered O and other points are associated with the name of the line, such as: ∠POQ

Types of Angles

  • Complementary Angles: The sum of two angles is 90°.
  • Supplementary Angles: The sum of two angles is 180°.
  • Adjacent Angles: Have common arms and are next to each other.
  • Linear Pair: The sum of two adjacent angles is 180°.
  • Vertically Opposite Angles: Formed when two lines intersect and are equal to each other.
  • Corresponding Angles: When a transversal cuts two parallel lines, the angles in the same direction are equal.
  • Alternate Interior Angles: When a transversal cuts two parallel lines, the alternate interior angles are equal.
  • Alternate Exterior Angles: The alternate exterior angles are equal.
  • Interior Angles on the Same Side of the Transversal: The sum of the interior angles on the same side is 180°.

Exercise 5.1

Question 1: Which pairs are complementary and which are supplementary?

  • Complementary Angles: The sum should be 90°.
  • Supplementary Angles: The sum should be 180°.

Exercise 5.2

Question 4: State the arms of two angles

  • Arms: DE and EF are common arms. Both angles share the same line.

Question 5: Value of angles.

  • Using the concept of a linear pair, calculate the value of the angles. For example: ∠A = 55°, ∠D = 125°, ∠B = 125°,

Question 6: Are L and M parallel?

  • First Figure: No, because the intersecting lines do not make supplementary angles.
  • Second Figure: No, corresponding angles are not equal to 75°.
  • Third Figure: Yes, the sum of corresponding angles is 180° and 70° on each side.
  • Fourth Figure: No, the sum of supplementary angles is 170°.

Important Points to Remember

  • Corresponding angles and alternate interior/exterior angles are equal.
  • The sum of linear pairs and interior angles on the same side of the transversal is 180°.
  • Vertically opposite angles are equal to each other.