Mechanical Linkages: Similar Triangles


This unit 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 folding umbrellas and car jacks and are built using the geometry of triangles and quadrilaterals. They offer rich potential for investigating geometry, starting with real-life objects, then making working models and then using pre-prepared dynamic geometry software. This unit looks at the geometry behind ironing tables and pantographs. The properties of similar triangles help to explain why an ironing table stays horizontal when the height is adjusted, and how a pantograph enlarges a drawing. The two lessons are independent of each other, so either one or both can be taught. They are especially suitable for Year 9.

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


Lesson 1: Ironing Table

When an ironing table with legs that pivot is raised or lowered, the top always stays parallel to the floor. In this lesson students investigate the triangles formed by the pivoting legs. They make physical models, observe computer simulations and explain with geometry why the table is always horizontal. Students investigate different leg lengths and pivot positions to ensure similar or congruent triangles are formed. Three designs of ironing table are included, involving different geometry.

Lesson 2: Pantograph

Students construct a physical model of an enlarging pantograph and use a computer simulation to explore how the copied image compares with the original drawing. They use their knowledge of parallelogram properties and similar triangles to explain how the pantograph works. By investigating pantographs further, students can extend their understanding of scale factors, generalise earlier findings and can design their own pantographs.


Last updated December 11 2018.