Chapter 16: Angles, polygons and geometrical reasoning
The chapter problem: a tiled courtyard
A designer plans a pattern with a straight path crossing a triangular tile. Some angles are marked, while others are hidden. How can you find every missing angle and explain why the answers must be correct?
First contact — estimate or notice. Imagine a straight line meeting another line. What might the two angles on one side add to? You do not need to calculate anything yet.
By the end of this chapter, you will use angle facts to solve the courtyard problem and explain each step.
By the end of this chapter you will be able to
- use angles at a point and on a straight line;
- identify corresponding, alternate and co-interior angles in parallel lines;
- use angle sums in triangles and quadrilaterals;
- find and use interior and exterior angle sums in polygons;
- write a geometrical argument with a reason for each step.
Roadmap
- 16.1 Angle facts at a point and on a line
- 16.2 Angles in parallel lines
- 16.3 Angles in triangles and quadrilaterals
- 16.4 Angles in polygons
- 16.5 Geometrical reasoning and proof (Higher only)
- Review
At Progress checks, return to the pattern and add a reason to your angle calculation.
Your turn to connect it
Where have you seen a tiled pattern, road junction or frame made from straight edges? Write one sentence about where angle reasoning could help you or someone you know.
The Learn pages teach each fact. Practise with help pages fade support, then Practise pages let you work independently.