Topic 5: Geometry and Measures

• A tangent and a radius meet at 90 degrees.
• two radii form an isosceles triangle
• the perpendicular bisector of a chord passes through the centre of the circle
• the angle at the centre of a circle is twice the angle at the circumference
• the angle in a semicircle is 90 degrees
• angles in the same segment are equal to 180 degrees.
• opposite angles in a cyclic quadrilateral add up to 180 degrees
• tangents from the same point are the same length
• the alternate segment theorem states that the area of a segment is equal to the sum of the areas of the alternate segments
• area of a triangle: 1/2 x base x height
• area of a parallelogram: base x vertical height
• area of a trapezium: average of parallel sides x distance between them (vertical height)
• area of a circle: pi x radius squared
• circumference: pi x diameter
• area of sector: x/360 x area of full circle
• length of arc: x/360 x circumference of full circle
• surface area of a sphere: 4 x pi x radius squared
• surface area of a cone: 1/3 x height x base x 2 x radius
• the surface area of a cylinder: pi x r^2 x 2 + 2 x pi x radius x height
• volume of a sphere: 4/3 x pi x r^3
• volume of a cone: (1/3) x base x height
• volume of a cylinder: base x height
• volume of pyramid: 1/3 x base area x vertical height
• volume of frustum: volume of original cone - volume of removed cone

  1/3 x pi x r^2 x h. - 1/3 x pi x r^2 x h
• Pythagoras' theorem: a^2 + b^2 = c^2
• finding angle = sin-1(x/y)
• the sine rule: a/sinA = b/sinB = c/sinC
• the "normal" cosine rule: a^2 = b^2 + c^2 - 2bc cosA
• cosine re-arranged: cosA = b^2+c^2-a^2/2bc
• area of triangle: 1/2 x a x b x sinC