Create FREE 'HowTo' Videos with MyGuide

Angles



Pass Quiz and Get a Badge of Learning



Content "filtered", Please subscribe for FULL access.


Chapter 2 : Angles



Angle arrow_upward


  • An Angle is a figure formed by two rays with the same initial point.
    • The initial point is called the Vertex.
    • The two rays are called the Arms of the angle.

  • It is generally represented by a symbol .

  • Types of Angles arrow_upward



    Acute Angle

  • An angle that measures between  and  is called an Acute angle.
  • For example:  is an Acute Angle.

  • Obtuse Angle

  • An angle that measures between  and  is called an Obtuse angle.
  • For example:  is an Obtuse Angle.

  • Reflex Angle

  • An angle that measures between  and  is called a Reflex angle.
  • For example:  is a reflex angle.

  • Straight Angle

  • An angle that measures exactly  is called a Straight Angle.
  • Straight (or Flat) angles are formed when the legs are pointing in exactly opposite directions.
    • The two legs then form a single straight line through the vertex of the angle.
    • The measure of a flat angle is thus always 180°.

    Complete Angle

  • An angle that measures exactly  is called a Complete angle.

  • Right Angle

  • An angle that measures exactly  is called a Right angle.
  • For example:  is a right angle.

  • Pair of Angles arrow_upward



    Angle Pair

    Property

    Adjacent Angles

  • Angles that have a common vertex and a common arm but no common interior.
  •  is adjacent to .
  • Vertically Opposite Angles

  • A pair of non-adjacent angles formed by the intersection of two straight lines.
  • Each opposite pair are called vertically opposite angles and are always congruent.
  •  For example:
  • ∠AOC and ∠BOD are vertically opposite angles.
  • Complementary Angles

  •  Two angles that add up to 90°. For example, the sum of ∠a and ∠b is 90°.
  • Supplementary

    Angles

  • Two angles that add up to 180°. For example, the sum of ∠a and ∠b is 180°.


  • Degree Measure of an Angle arrow_upward


  • The standard unit of measurement of an angle is Degree.
  • It is represented by symbol of “ .
    • 1 Right Angle = 90°= 90 Degree
    • 1 Degree = 60 Minutes

    Transversal arrow_upward


  • A transversal is a line that crosses at least two other lines.

  • Transversal Intersecting Non Parallel Lines

  • Here AB is a transversal which intersects two non parallel lines PQ and RS.

  • Transversal Intersecting Parallel Lines

  • Here AB is a transversal which intersects two parallel lines PQ and RS.

  • Vertically Opposite Angles arrow_upward


  • Vertical Opposite Angles are the angles opposite to each other when two lines cross.
  • They are called “Vertical” because they share the same vertex.
  • Here  are vertical opposite angles.
  • For example, if a and d are vertical angles, the measure of both a and d will be same.

  • Interior Angles of a Transversal arrow_upward


  • Angles that are formed on the inside of the two lines are known as Interior angles.
  • Here   are interior angles.

  • Exterior Angles of a Transversal arrow_upward


  • Angles that are formed on the outside of the two lines are known as Exterior angles.
  • Here   are exterior angles.

  • Corresponding Angles arrow_upward


  • If two lines are parallel, the pairs of angles on the same side of the transversal if both lie either above the two lines or below the two lines.
  • Two line are intersected by a transversal such that  .

  • Alternate Interior and Exterior Angles arrow_upward


  • Alternate Interior Angles are created where a transversal crosses two (usually parallel) lines.
    • Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.
  • In the diagram below   are Alternate Interior Angles.
  • Alternate Exterior Angles are created where a transversal crosses two (usually parallel) lines.
    • Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal.
  • And   are Alternate Exterior Angles.

  • Theorems: Angles arrow_upward



    Property 1

  • For parallel lines, Pairs of alternate (interior or exterior) angles are equal.

  • Property 2

  • For parallel lines, Pairs of corresponding angles are equal.

  • Property 3

  • The sum of the interior (or exterior) angles on the same side of the transversal is.

  • Angle Bisector arrow_upward


  • A ray that divides an angle into two equal and adjacent angles is called as an Angle Bisector.
  • Angle bisector divides the angle AXC into two equal parts such that

    ∠AXB = ∠BXC.



    Thank You from Kimavi arrow_upward


  • Please email us at Admin@Kimavi.com and help us improve this tutorial.


  • Mark as Complete => Receive a Certificate in Geometry


    Kimavi Logo

    Terms and conditions, privacy and cookie policy | Facebook | YouTube | TheCodex.Me | Email Kimavi


    Kimavi - An AI Powered Encyclopedia { Learning is Earning }

    Get Ad Free Encyclopedia with Progress Report, Tutor Help, and Certificate of Learning for only $10 a month



    All videos on this site created using MyGuide.

    Create FREE HowTo videos with MyGuide.