What's the story on this
notation between things that are congruent and those that are
equal?
The notation used in geometry can often be
confusing. The major problems seem to develop when working
with segments and angles. Let's see if we can clarify "what"
gets used "when".


Basic
knowledge: 

with the bar on top, means the actual segment
itself.


without the bar on top, means the length of the
segment labeled A and B. 


means the actual angle itself.


means the measure of the angle labeled A, B and
C. 

When to use congruent: 
When to use equal: 
Figures are congruent.
Segments are congruent. Angles are congruent.
Triangles are congruent. This refers to the actual diagrams themselves.

Numerical values are equal.
When an expression represents a length or measure, equal
should be used.

Notation at Work: 
Things
you should and should not write: 
Let's see what we should write if we wish to
add the lengths of two sets of segments known to be congruent:

Before we try to add these statements, we need
to change these congruent entities to numerical
values. After all, we add numbers, not sets of
points.


Congruent segments are segments of
equal measure. 
Now that we have these numerical
values, we are ready to add: 



NO


YES


NO 

YES


NO 
and

YES


NO 

YES 

NO 

YES 

YES 

Textbooks may vary on how they represent notation.
Listen to your teacher as to how he/she wants you to use
geometrical notation, especially when writing proofs.
All proofs on this web site will follow the notation
described above. 
