Lines and Angles

Line Segment is the portion of the line between two points A and B. A line segment has two end points. Ray is a line segment AB when extended in one direction.

An infinite number of lines can be drawn through a point. All lines are called concurrent lines. One and only one line can be drawn passing through two given points.

If a line can pass through three or more points, then these points are said to be collinear points, otherwise points are non-collinear.

Two lines are called parallel lines if both have no points in common or if the distance between the lines is same everywhere.

Angle is formed by two rays with a common initial point called vertex and measured in degrees.

  1. Acute angle: An angle whose measure is less than 90º.
  2. Right angle: An angle whose measure is 90º.
  3. Obtuse angle: An angle whose measure is more than 90º but less then 180º.
  4. Straight angle: An angle whose measure is 180º.
  5. Reflex angle: An angle whose measure is more than 180º and less than 360º.

Two lines or rays making a right angle with each other are called perpendicular lines.

Complementary angles: Two angles are complementary if the sum of their measures is 90º.

Supplementary angles: Two angles are supplementary if the sum of their measures is 180º.

Adjacent angles: Two angles having a common vertex, a common arm and non common arms on opposite sides of the common arm.

When a transversal intersects two parallel lines, then

  1. each pair of corresponding angles are equal.
  2. each pair of alternate angles are equal.
  3. each pair of interior angles on the same side of the transversal are supplementary.

For example:

  1. ∠2 = ∠6, ∠3 = ∠7
  2. ∠3 = ∠6 and ∠4 = ∠5
  3. ∠3 + ∠5 = 180º and ∠4 + ∠6 = 180º