Topics covered within this unit: 30·1 Constructions revision 30·2 Further constructions 30·3 Theorems revision 30·4 Similar triangles
The Learning Outcomes covered in this unit are contained in the following sections:
GT.3a GT.3b.II GT.3c
Key words Similar triangles
Pyramid Thales 1.8 m 98 m 1.2 m
Further geometry
Something to think about …
Thales, a Greek mathematician, is credited with fi nding an easy way to calculate the height of the pyramids of Egypt using shadows.
He worked it out by fi nding the ratio of his height to the length of his shadow at a certain time of the day.
Using this ratio and the length from the centre of the pyramid to the end of its shadow at the same time of the day, he calculated the height of the pyramid.
Imagine Thales was 1·8 m tall and his shadow was 1·2 m long.
At the same time, the distance from the centre of the pyramid to the end of its shadow was 98 m. Use this information to calculate the height of the pyramid.
30·1 Constructions revision
By the end of this section you should: ● recall how to complete constructions 1, 2, 4, 5, 8, 9, 10, 11, 12, 13, 14 and 15
In this unit, we will revise all the constructions and theorems you have done so far and complete the remaining constructions and theorems for your course.