5 Geometry of Lines, Triangles and Circles
One can hardly get more practical than surveying and designing buildings and other struc-
tures and geometry underpins all these and much more, such as computer aided design.
This chapter consolidates the key areas of basic geometry. It is relatively elementary
in content, but not in concepts, some of which are found to give students considerable
difficulty. Here these are covered concisely, offering plenty of practice.
Prerequisites
It will be helpful if you know something about:- ratio and proportion (14
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) - measurement of angles
- elementary properties of triangles
- Pythagoras’ theorem
- area and perimeter of a circle
- solution of algebraic equations (Chapter 2
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)- elementary algebra (Chapter 2
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)Objectives
In this chapter you will find:- division of a line in a given ratio
- intersecting and parallel lines and angular measurement
- triangles and their elementary properties
- congruent triangles
- similar triangles
- the intercept theorem
- the angle bisector theorem
- Pythagoras’ theorem
- lines and angles in a circle
- cyclic quadrilaterals