Study Notes
Polygons are 2-dimensional closed shapes made of straight lines. Regular polygons have all sides and angles equal, while irregular polygons do not.
- Quadrilateral — a polygon with four sides, vertices, and angles. Example: The sum of interior angles is 360°.
- Square — a quadrilateral with all sides equal and all angles 90°. Example: It has four lines of symmetry and rotational symmetry of order 4.
- Rectangle — a quadrilateral with opposite sides equal and all angles 90°. Example: It has two lines of symmetry and rotational symmetry of order 2.
- Parallelogram — a quadrilateral with opposite sides parallel and equal. Example: Opposite angles are equal, and it has rotational symmetry of order 2.
- Rhombus — a parallelogram with all sides equal. Example: Diagonals bisect at right angles.
- Trapezium — a quadrilateral with one pair of parallel sides. Example: It has no line or rotational symmetry.
- Kite — a quadrilateral with two pairs of adjacent sides equal. Example: It has one line of symmetry and no rotational symmetry.
- Interior Angles — the sum of interior angles of a polygon is (n − 2) × 180°. Example: For a pentagon, the sum is 540°.
- Exterior Angles — the sum of exterior angles of any polygon is 360°. Example: For a regular pentagon, each exterior angle is 72°.
Exam Tips
Key Definitions to Remember
- A quadrilateral is a polygon with four sides.
- Regular polygons have all sides and angles equal.
- The sum of interior angles of a polygon is (n − 2) × 180°.
- The sum of exterior angles of any polygon is 360°.
Common Confusions
- Confusing regular and irregular polygons.
- Forgetting that the sum of exterior angles is always 360°.
Typical Exam Questions
- What is the sum of the interior angles of a hexagon? Answer: 720°
- How many sides does a regular polygon have if each exterior angle is 30°? Answer: 12 sides
- Calculate the size of each interior angle of a regular octagon. Answer: 135°
What Examiners Usually Test
- Understanding of properties of different quadrilaterals.
- Ability to calculate unknown angles in polygons.
- Application of angle sum formulas for polygons.