Geometry for Elementary School/Conventions

This appendix summarises the conventions used in this book. There is also a British-American English differences table provided.

Language

All the language in this book uses simple British English. Alternative names in American English are listed below.

British English	American English	Other names
Vertically opposite angles	Vertical angles	/
The right angle-hypotenuse-side congruence theorem (RHS)	The hypotenuse-leg congruence theorem (HL)	The hypotenuse-leg-right angle theorem (HLR)
Centre	Center	/
Compass	Compass	A pair of compasses (British)
Trapezium	Trapezoid	/
Centimetre / Millimetre / Metre / Kilometre	Centimeter / Millimeter / Meter / Kilometre	/
Millilitre / Litre	Milliliter / Liter	/

Notation

This appendix summarises the notation used in the book. An effort was made to use common conventions in the notation. However, since many conventions exist the reader might see a different notation used in other books.

Point

A point will be named by an uppercase letter in italics, as in the point A. In some equations though, it will look like this: $A$.

Line segment

We will use the notation ${\overline {AB}}$ for the line segment that starts at A and ends at B. Note that we don't care about the segment direction and therefore ${\overline {AB}}$ is similar to ${\overline {BA}}$.

Angles

We will use the notation $\angle {ABC}$ for the angle going from the point B, the intersection point of the segments ${\overline {BA}}$ and ${\overline {BC}}$. Sometimes the angle may also be represented by a lowercase letter or even a number, but this is only used in the main text for ease and not in the exercises.

Triangles

A triangle whose vertices are A, B and C will be noted as $\triangle ABC$. Note that for the purpose of triangles' congruence, the order of vertices is important and $\triangle ABC$ and $\triangle BCA$ are not necessarily congruent.

Circles

We use the notation $\circ A,{\overline {BC}}$ for the circle whose center is the point A and its radius length equals that of the segment ${\overline {BC}}$.

Note that in other sources, a circle is described by any 3 points on its circumference, ABC. The center, radius notation was chosen since it seems to be more suitable for constructions.

External links

If you are interested seeing an example of past notation, you might be interested in Byrne's edition of Euclid's Elements. See for example the equilateral triangle construction.