Notation
Geometry Index | Regents Exam Prep Center

 

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.