# 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

- Given by a vector
- Rotations
- 3 details
- Angle of rotation
- Direction of rotation
- Centre of rotation

- 3 details
- 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

- Scale factor

- Translations
- 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

- SSS

- 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

- Parallelogram
- 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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