#### 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*.

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)

- External angles =

- 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.