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Geometry

TRIANGLES

QUADRILATERALS
  • Rectangle: Opposite sides are parallel and equal, all angles 90°. The diagonals bisect each other.
  • Parallelogram: Opposite sides are parallel and equal, opposite angles are equal, diagonals bisect each other.
  • Rhombus: is a  parallelogram with all sides equal. Its opposite angles are equal, its diagonals bisect each other.
  • Trapezium: One pair of its sides are parallel.
  • Kite: Two pairs of its adjacent sides are equal, its diagonals meet at right angles, bisecting one of them.
SYMMETRY
  • A line of symmetry divides a two-dimensional shape into two congruent (identical) shapes.
  • A plane symmetry divides a three-dimensional shape into two congruent solid shapes.
  • The number of times a shape fits its outline during a complete revolution is called the order of rotational symmetry.
ShapeNumber of Lines of SymmetryRotational Symmetry Order
Square44
Rectangle22
Parallelogram02
Rhombus22
Trapezium01
Kite11
Equilateral Triangle33
Regular Hexagon06

 

  • Properties of circles:
    • Equal chords are equidistant from the center.
    • The perpendicular bisector of a chord passes through the center.
    • Tangents from an external point are equal in length.
  • Sum of angles at a point = 360°
  • Angles on a straight line = 180°
  • Sum of angles in a triangle = 180°
  • For regular polygons:
    • External angles = 360/n
    • Sum of interior angles = 180(n – 2)
  • Vertically opposite angles (X1-X1, X-X)
  • Corresponding angles
  • Alternate angles
  • Co-interior angles
  • Exterior angle = Sum of interior angles opposite the exterior angle. (d = a + b)
CIRCLE THEOREM

LOCI
  • The locus of points equidistant from a point is a circle.
  • The locus of points equidistant between two points is a perpendicular bisector.
  • The locus of points equidistant between two lines is an angle bisector.
  • The locus of points equidistant (along) from a line is a parallel line.
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