General Geometric Shapes
Square
- All sides are equal
- Opposite sides are parallel
- Each interior angle is a right angle (90º)
- The interior angles total up to 360º
- Diagonals bisect each other at right angles.
- Diagonals measure the same length and bisect interior angles.
Rectangle
- Each interior angle is 90º and they all add up to 360º
- Diagonals are equal
- Diagonals bisect each other but NOT at right angles
Parallelogram
- Opposite sides are equal and parallel
- Opposite angles are equal
- Diagonals bisect each other
- Diagonals are not equal
- Adjacent angles are supplementary (add up to 180º)
Rhombus
- All sides are equal
- Opposite sides are parallel
- Opposite angles are equal
- Diagonals bisect each other at 90º
- Diagonals bisect the interior angles
Trapezium
- The sum of the interior angles is 360º
- Has a pair of parallel lines which are not of the same length
- Has a perpendicular height joining the two parallel lines
Right-angled Triangle (Pythagorean relationship)
- H2 = b2 + h2
- b2 = H2 – h2
- H2 = H2 - b2
Examples of relationships
Base Height Hypotenuse 3 4 5 6 8 10 5 12 13 7 24 25 8 15 17 9 40 41
Properties of Triangles and Parallel Lines
Triangle
Exterior angles & interior angles
- Angles x, y, and z are exterior angles while a, b, and c are interior angles.
- Exterior angles add up to 360º while interior angles add up to 180º.
- Angles x, a; b, z; and c, y; are adjacent to each other and they add up to 180º (supplementary angles)
Parallel Lines and Transversal
- Angles at a point e.g. a + b+ c + d = 360º
- Vertically opposite e.g. a/d, b/c, f/g, e/h. They are equal
- Corresponding angles e.g. b/f, a/e, c/g, d/h. They are equal
- Alternate angles e.g. c/f, d/e are always equal.
- Co-interior angles e.g. c/e, d/f, are always equal.
- Co-interior/allied angles e.g. c/e, d/f are formed by parallel lines. They are supplementary.
Speed, Distance and Time
The formulae related to speed, distance and time can be derived from the following triangle.