Notation (the figure vs its measure)

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The notations used in geometry can be a bit confusing at first.
Basically, there are notations that refer to the actual geometric figures (the drawings), and there are notations that refer to the measures (sizes, lengths) of the figures.

ab is a segment.
The bar over the letters means you
are referring to the segment itself
(the actual physical segment).
AB is a length, a number.
The letters, without a bar on top, refer to the length of the segment
from point A to point B.

ab is an angle.
The angle symbols,angsymbols, mean you are referring to the angle itself (the actual physical angle).

abis a measure, a number.
The m in front of the angle notation refers to the measure of the angle labeled A, B and C (with vertex at B).

By definition, the term congruent means "having equal length or measure".

Figures are congruent (congruent14).
Segments are congruent. Angles are congruent. Triangles are congruent. The congruent symbol is used when referring to the actual physical entities (diagrams).congruent3
Numerical values are equal. (=)
When referring to a length or measure, the equal sign should be used. You speak of numbers as being equal (or not equal).
(Triangles are not referred to as being "equal", since they are not numbers, and we do not speak of the measure of a Δ.)

Let's look at the notation needed when we want to say that the lengths of the sections of this segment equal the length of the entire segment.

Given ab12.
We can observe from the diagram that AB = 3 and BC = 8.
Consequently, AC = 11. (The whole is equal to the sum of its parts.)
Write:   AB + BC = AC.          Do NOT write: wholeNOa
You add the segment lengths. You cannot "add" the actual segment diagrams.

While most textbooks follow this notation process,
you may find some sources that show varying notations.
This web site will be following the notations as described on this page.


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