Triangles & polygons
Triangles and polygons are hiding everywhere — in roofs, road signs, honeycomb and football patterns. In this lesson we name the four types of triangle and learn that their angles always add up to 180°, then meet the clever exterior-angle rule. We move on to quadrilaterals and their 360° angle sum, plus the special ones — square, rectangle, parallelogram, rhombus, trapezium and kite — and their properties. Finally we open up to many-sided polygons and the tidy formulas: the interior angle sum (n − 2) × 180°, the exterior angles that always add to 360°, and how to find each angle, or the number of sides, of a regular polygon. Throughout, we practise finding missing angles step by step, always writing the reason in words the way the marker wants.
By the end you should be able to (NSSCO Mathematics 5.2):
- Name the four types of triangle: equilateral, isosceles, scalene and right-angled
- Use the rule that the angles in a triangle add up to 180°
- Use the exterior angle of a triangle = the sum of the two interior opposite angles
- Name the special quadrilaterals and state their properties: square, rectangle, parallelogram, rhombus, trapezium and kite
- Use the rule that the angles in a quadrilateral add up to 360°
- Find the interior angle sum of a polygon using (n − 2) × 180°
- Find each interior and exterior angle of a regular polygon, using the fact that exterior angles add up to 360°
- Find the number of sides of a regular polygon from its interior or exterior angle
Miss Jay Jay and Mike talk through the whole topic — with the figure and working drawn live.