MATHEMATICS

• Point


  A point has location only but has no size nor shape. It can be modelled by a dot. A point is named using a capital letter.
• Line


  A line is a straight continuous arrangement of infinitely many points. Its length is infinite. It extends indefinitely in two directions. It has no thickness. A line is named by a single lower case script letter or by any two points on a line.
• Subsets of a Line

  • Line segment
  • Ray
  • Line
• Line segment


  A line segment is a part of a line consisting of two endpoints and all the points in between.
• Ray


  A ray is a part of a line with only one endpoint and extending in only one direction.
• Plane


  A plane is a flat surface that extends infinitely along its length and width. It has length and width but has no thickness. A plane is named by a single script capital letter or by any three points in the plane which are not on the same line.
• Intersecting lines


  Intersecting lines are lines on the same plane having a common point.
• Parallel lines


  Parallel lines are lines on the same plane that do not intersect. They are always the same distance apart.
• Perpendicular lines


  Perpendicular lines are intersecting lines that form right angles.
• Collinear


  Collinear means on the same line.
• Coplanar


  Coplanar means on the same plane.
• Angle


  An angle is formed by two non-collinear rays with a common endpoint. The two rays are the sides of the angle. The common endpoint of the two rays is the vertex of the angle.
• Three ways of Naming Angles

  • Using three capital letters
  • Using the vertex
  • Using a number or symbol at the vertex
• Measuring Angles


  The measure of an angle is determined by the amount of opening of its sides. We use protractor to determine the measure of the angle in degrees (°).
• Kinds of Angles


  • Acute angle
  • Right angle
  • Obtuse angle
• Acute angle


  An angle whose measure is less than 90° but greater than 0°.
• Right angle


  An angle whose measure is exactly 90°.
• Obtuse angle


  An angle whose measure is more than 90° but less than 180°.
• Acute, right, and obtuse angles

  • Acute angles: ∠FMG, ∠HMI

  Right angle: ∠GMH

  Obtuse angles: ∠FMH, ∠GMI
• Complementary angles


  Two angles are called complementary if their sum is 90°.
• Complementary angles


  • 25° + 65° = 90°

  60° + 30° = 90°
• Find the value of x in the complementary angles example

  x + 2x + 15 = 90

  3x + 15 = 90

  3x = 75

  x = 25
• Supplementary angles


  Two angles are called supplementary if their sum is 180°.
• Supplementary angles


  • 60° + 120° = 180°

  110° + 70° = 180°
• Find the value of x in the supplementary angles example

  2x + 30 + x = 180

  3x = 150

  x = 50
• Adjacent angles


  Adjacent angles are two angles with a common vertex, a common side, but without common interior points.
• Linear pair


  Two angles form a linear pair when they are adjacent and supplementary.
• Determining if angles are adjacent and/or form a linear pair


  • ∠1 and ∠2 are not adjacent

  ∠2 and ∠3 are adjacent

  ∠1 and ∠3 are not adjacent

  ∠2 and ∠3 form a linear pair

  ∠1 and ∠2 do not form a linear pair
• Congruent angles


  Two angles are congruent if their measures are equal.
• Vertical angles


  When two lines intersect, the opposite angles are called vertical angles. These angles are always congruent.
• Finding measures of vertical angles

  • If m∠3 = 63, then m∠1 = 63, m∠2 = 117, and m∠4 = 117
• Find the value of x in the vertical angles example

  2x + 6 = 3x - 11

  17 = x