Angles, lines and shapes
Measuring and drawing angles, angles on parallel lines, triangles and quadrilaterals, angle sums of polygons and algorithms that sort shapes.
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Angles are everywhere: in the corners of a room, the hands of a clock, a roof truss and the lines on a road. In this topic you'll measure and draw angles with a protractor, discover the angle rules that appear when a line crosses parallel lines, and find out why the angles of every triangle add to 180°. You'll then use these facts to sort and reason about triangles, quadrilaterals and other polygons, and design your own step-by-step algorithms for sorting shapes.
What you'll learn
- 11.01 Measure angles: types of angles, measuring and drawing angles (including reflex angles) with a protractor, and angles on a line, at a point and vertically opposite.
- 11.02 Parallel lines and transversals: corresponding, alternate and co-interior angles, using them to find unknown angles, and deciding whether lines are parallel.
- 11.03 Triangles: naming triangles by their sides and angles, showing that the angles add to 180°, and finding unknown and exterior angles.
- 11.04 Quadrilaterals: the properties of squares, rectangles, rhombuses, parallelograms, trapeziums and kites, the 360° angle sum, and angle sums of other polygons.
- Investigation: follow, finish and design flowcharts that sort triangles and quadrilaterals by their properties.
Which level should I pick?
Every worksheet comes in three levels. Each one covers the same skills.
- Level 1 · Warm-up: simpler diagrams and more help along the way. A good place to start.
- Level 2 · Core: the main worksheet for the lesson.
- Level 3 · Challenge: multi-step problems, algebra and explaining why the angle rules work, for when the Core level feels easy.
Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes. You'll need a ruler and a protractor. Print the worksheets at full size (100%) so the angles you measure are drawn at their true size.
Practice tests
When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.
Curriculum outcomes
What this topic covers in the Australian Curriculum (version 9).
identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons
demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles
classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships
design and create algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work
From earlier years: these lessons revise skills students learnt in earlier years that this year's curriculum builds on, so they aren't linked to an outcome code for this year.
Outcomes lesson by lesson
- 11.01 Measure anglesFrom earlier years
- 11.02 Parallel lines and transversalsAC9M7M04
- 11.03 TrianglesAC9M7M05AC9M7SP02
- 11.04 QuadrilateralsAC9M7M05AC9M7SP02
- Investigation: Sort shapes with algorithmsAC9M7SP04