# Mechanical Linkages: Angles and Lines

ACMMG164; ACMMG165

This 2-lesson unit for Year 7 is part of the special topic “Mechanical Linkages and Deductive Geometry”. Mechanical linkages – sets of hinged rods – form the basis of many everyday objects such as ironing tables and car jacks and are built using the geometry of triangles and quadrilaterals. They offer rich potential for investigating geometry, with real -life objects, working models and then with pre-prepared dynamic geometry software. This unit investigates side lengths of triangles and angles. There are opportunities to develop geometric language and to highlight how mathematical structures such as points, lines and angles can be seen in real objects, linking geometry diagrams with real things.

Read the Teachers' Guide, included in the unit download, for teaching advice and practical hints for the constructions.

### Lesson 1: Folding Quadrilaterals

Students make models of triangles and quadrilaterals, using strips hinged with paper fasteners. In a series of five challenges, they investigate the relationships between the lengths of strips that can make triangles and quadrilaterals. They contrast the rigidity of triangles with the flexibility of quadrilaterals. They then investigate what quadrilaterals fold neatly. An introduction to mechanical linkages can be included.

### Lesson 2: An Extended Protractor

Students explore the unique design of an extended protractor that has a rhombus linkage attached to it. This award-winning design (CCKL-Creator) enables easy measuring of inside and outside angles in both two-dimensional and three-dimensional situations. Students construct a physical model of the extended protractor and observe angle sizes in a computer simulation. They identify the relationships between angles formed by the parallel lines in the protractor, and use the equalities to explain how the extended protractor works.

Last updated December 5 2018.