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#### Geometry

##### TRIANGLES • 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. Shape Number of Lines of Symmetry Rotational Symmetry Order
Square 4 4
Rectangle 2 2
Parallelogram 0 2
Rhombus 2 2
Trapezium 0 1
Kite 1 1
Equilateral Triangle 3 3
Regular Hexagon 0 6

• 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. 