MATH

• Circle


  Set of all points in a plane at a given distance from a fixed point (the center)
• Circle


  • Named using its center
  • Radius is a line segment from the center to any point on the circle
• Parts of a circle

  • Radius
  • Diameter
  • Chord
  • Center
  • Arc
  • Central angle
• Radius


  Line segment from the center to any point on the circle
• Chord


  Line segment whose endpoints lie on the circle
• Diameter


  Chord that passes through the center of the circle
• Arc


  Continuous part of the circle between two points on the circle
• Semi-circle


  Arc whose endpoints are the points of a diameter
• Minor arc


  Arc less than half the circle, can be named using 2 or 3 points
• Major arc


  Arc greater than half the circle, must be named using 3 points
• Central angle


  Angle whose vertex is the center of the circle
• Inscribed angle


  Angle whose vertex is on the circle
• Central angle


  Measure of central angle = measure of intercepted arc
• Inscribed angle


  Measure of inscribed angle = 1/2 measure of intercepted arc
• Secant


  Line that intersects the circle in two points
• Tangent


  Line that intersects the circle in exactly one point (the point of tangency)
• Congruent circles


  Two or more circles with equal radii
• Concentric circles


  Two or more circles with the same center but different radii
• Polygon


  A closed shape with straight sides
• Finding the sum of interior angles of a triangle

  1. Draw triangle

  2. Cut along dotted lines to separate angles

  3. Arrange angles without overlapping

  4. Use protractor to measure angles
• The sum of the three interior angles of a triangle is 180 degrees
• Solving for missing angle in a triangle

  1. Add the two given angles

  2. Subtract the sum from 180 degrees
• Solving for missing angle in a triangle

  • 38 degrees + 105 degrees = 143 degrees, missing angle is 37 degrees
  • 65 degrees + 65 degrees = 130 degrees, missing angle is 50 degrees
  • 90 degrees + 25 degrees = 115 degrees, missing angle is 65 degrees
  • 110 degrees + 41 degrees = 151 degrees, missing angle is 29 degrees
  • 38 degrees + 49 degrees = 87 degrees, missing angle is 93 degrees
• Finding the sum of interior angles of a convex polygon

  1. Draw all possible diagonals from one vertex

  2. Polygon is divided into triangles

  3. Sum of interior angles = Number of triangles x 180 degrees
• The sum of the interior angles of a convex polygon with n sides is (n-2) x 180 degrees
• Sum of interior angles of polygons

  • Triangle: 3 sides, 1 triangle, 180 degrees
  • Quadrilateral: 4 sides, 2 triangles, 360 degrees
  • Pentagon: 5 sides, 3 triangles, 540 degrees
  • Hexagon: 6 sides, 4 triangles, 720 degrees
  • Heptagon: 7 sides, 5 triangles, 900 degrees
  • Octagon: 8 sides, 6 triangles, 1080 degrees
  • Nonagon: 9 sides, 7 triangles, 1260 degrees
  • Decagon: 10 sides, 8 triangles, 1440 degrees
• The number of triangles formed in a polygon with n sides is n-2
• Calculating sum of interior angles

  • Dodecagon (12 sides): 10 triangles, 1800 degrees
  • 20-gon (20 sides): 18 triangles, 3240 degrees
• Regular polygon


  A polygon with congruent sides and congruent angles
• The measure of each interior angle of a regular triangle is 60 degrees
• Solving for missing angle in a quadrilateral

  1. Sum of interior angles is 360 degrees

  2. Add given angles

  3. Subtract sum from 360 degrees to find missing angle
• Solving for missing angle in a quadrilateral

  • 119 degrees + 107 degrees + 78 degrees = 304 degrees, missing angle is 56 degrees
• Solving for missing angle in a hexagon

  • 98 degrees + 109 degrees + 95 degrees + 153 degrees + 165 degrees = 620 degrees, missing angle is 100 degrees
• Exterior angle


  Angle formed by one side of a polygon and an extended adjacent side
• The sum of the exterior angles of any convex polygon is 360 degrees
• Exterior angles of a triangle

  • Angle 1: 115 degrees
  • Angle 2: 115 degrees
  • Angle 3: 130 degrees
• Exterior angles of a hexagon

  • 82 degrees + 71 degrees + 85 degrees + 27 degrees + 80 degrees + 15 degrees = 360 degrees
• An interior angle and an exterior angle on the same vertex are supplementary, their sum is 180 degrees
• Polygon


  A close plane figure bounded by segments, with three or more non-collinear segments joined at their endpoints (called sides), three or more endpoints on their sides (called vertices), and three or more angles
• Polygon literally means "many sides"