Tests for special quadrilaterals: Parallelograms: Co-ordinate Geometry Two opposite sides equal and Straight line parallel or Gradient form: y = m + b Opposite sides are equal or General form: A + By + C = 0 Opposite angles are equal or Diagonals bisect each other Distance: d = (1-2)2 + (y1-y2)2 Rhombus: All sides equal or Midpoint: mp = (1 + 2 , y1 + y2 ) Diagonals bisect each other at right angles Rectangle: All angles are right angles or Gradient: m = y2-y1 Parallelogram with equal diagonals 2-1 Square: All sides equal and one angle right Perpendicular distance or P = A1 + By1 + C All angles right and two adjacent sides equal. A2 + B2 Tests for congruent triangles SSS m = tan SAS AAS RHS Geometrical Properties Tests for similar triangles Complementary angles add to 90 AA Supplementary angle add to 180 Corresponding sides proportional Vertically opposite angles are equal (SSS) Angles at a point add to 360 Two sides are proportional and Angle sum of a triangle is 180 included angles are equal (SAS) The exterior angle of a triangle is equal to the sum of the opposite Applications of Differentiation interior angles First derivative dy/d An isosceles triangle has equal base - Stationary point when equals 0 angles - Curve increasing>0 Equilateral triangles have all angles - Curve decreasing<0 60 -Max turning point if second Alternate angles on parallel lines are derivative negative equal -Minimum turning point if second Corresponding angles on parallel derivative positive lines are equal Second derivative d2y/d2 Co-interior angles between parallel - Point of inflexion when equals 0 lines are supplementary -Concave up when >0 The angle sum of a polygon is -Concave down when <0 (n-2)x180 Horizontal point of inflexion if both The sum of the exterior angles of first and second derivative equals any polygon is equal to 360 zero. The angle sum of a quadrilateral is 360 Integration
Co-ordinate Geometry Straight line Gradient form: y = m + b General form: A + By + C = 0 Distance: d = (1-2)2 + (y1-y2)2 Midpoint: mp = (1 + 2 , y1 + y2 ) Gradient: m = y2-y1 2-1 Perpendicular distance P = A1 + By1 + C A2 + B2 m = tan Geometrical Properties Complementary angles add to 90 Supplementary angle add to 180 Vertically opposite angles are equal Angles at a point add to 360 Angle sum of a triangle is 180 The exterior angle of a triangle is equal to the sum of the opposite interior angles An isosceles triangle has equal base angles Equilateral triangles have all angles 60 Alternate angles on parallel lines are equal Corresponding angles on parallel lines are equal Co-interior angles between parallel lines are supplementary The angle sum of a polygon is (n-2)x180 The sum of the exterior angles of any polygon is equal to 360 The angle sum of a quadrilateral is 360 Tests for special quadrilaterals: Parallelograms: Two opposite sides equal and parallel or Opposite sides are equal or Opposite angles are equal or Diagonals bisect each other Rhombus: All sides equal or Diagonals bisect each other at right angles Rectangle: All angles are right angles or Parallelogram with equal diagonals Square: All sides equal and one angle right or All angles right and two adjacent sides equal. Tests for congruent triangles SSS SAS AAS RHS Tests for similar triangles AA Corresponding sides proportional (SSS) Two sides are proportional and included angles are equal (SAS) Applications of Differentiation First derivative dy/d - Stationary point when equals 0 - Curve increasing>0 - Curve decreasing<0 -Max turning point if second derivative negative -Minimum turning point if second derivative positive Second derivative d2y/d2 - Point of inflexion when equals 0 -Concave up when >0 -Concave down when <0 Horizontal point of inflexion if both first and second derivative equals zero. Integration