Geometry and measures

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  • Created by: joduffy
  • Created on: 20-04-15 11:33
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  • Geometry and measures
    • Exterior angle of a triangle = sum of opposite interior angles
    • Polygons
      • Sum of exterior angles = 360º
      • Sum of interior angles = (n-2) x 180º
        • N = no. of sides
      • Regular polygons only
        • Exterior angle = 360º ÷ N
        • Interior angle = 180º - exterior angle
    • Circle Theorems
      • A tangent and a radius meet at 90º
      • Two radii form an isoceles triangle
      • The perpendicular bisector of a chord passes through the centre of a circle
      • Angle at centre is twice angle at circumference
      • Angle in a semicircle is 90º
      • Angle in same segment are equal
      • Opposite angles in a cyclic quadrilateral add up to 180º
      • Tangents from the same point are the same length
      • Angle between a tangent and a chord is equal to angle in opposite segment
    • Transformations
      • Translations
        • Given by a vector
          • Left and down is negative
      • Rotations
        • 3 details
          • Angle of rotation
          • Direction of rotation
          • Centre of rotation
      • Reflections
        • Equation of mirror line
      • Enlargements
        • Scale factor
          • New length ÷ old length
          • Scale factor less than one = shape gets smaller
          • Negative scale factor = opposite side
        • Centre of enlargement
    • Congruent shapes
      • Same size, same shape
      • Prove triangles are congruent
        • SSS
          • Three sides are the same
        • AAS
          • Two angles and a corresponding angle side match up
        • SAS
          • Two sides and angle between them match up
        • RHS
          • Right angle, hypotenuse and one other side all match up
    • Areas
      • Parallelogram
        • A= b x h (vertical)
      • Trapezium
        • A= 1/2(a+b) x h(vertical)
      • Circle
        • pie x radius squared
        • Circumference = 2 x pie x radius
    • Volumes
      • Prism = cross sectional area x length
      • Cuboid =  Length x width x height
      • Sphere = 4/3 x pie x radius cubed
      • Cone= 1/3 x pie x radius squared x vertical height
      • Volume of pyramid= 1/3 x base area x vertical height
    • Surface area
      • Sphere = 4 x pie x radius squared
      • Cone = pie x raidus x length + pie x radius swuared
      • Surface area of cylinder = 2 x pie x radius x height + 2 x pie x radius sqaured

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