# Geometry and measures

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• Created by: joduffy
• Created on: 20-04-15 11:33
• 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
• 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
• 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