Properties of Geometric Shapes - Class 8 Mathematics Revision Notes

• General Geometric Shapes
  • Square
  • Rectangle
  • Parallelogram
  • Rhombus
  • Trapezium
  • Right-angled Triangle
  • Equilateral Traingle
  • Isosceles Triangle
• Properties of Triangles and Parallel Lines
  • Triangle
  • Parallel Lines and Transversal
• Speed,Distance and Time

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

1. Angles at a point e.g. a + b+ c + d = 360º
2. Vertically opposite e.g. a/d, b/c, f/g, e/h. They are equal
3. Corresponding angles e.g. b/f, a/e, c/g, d/h. They are equal
4. Alternate angles e.g. c/f, d/e are always equal.
5. Co-interior angles e.g. c/e, d/f, are always equal.
6. 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.