A "convention" is "just
the way a thing is done!" Unfortunately, sometimes conventions in
math are glossed over, and you're expected somehow "to just know"
what they are. If you, like me, missed some of the conventions that relate
the geometry and trigonometry, please review the following.

In geometrical pictures (or "figures",
in the parlance), points are customarily labelled with capital Latin letters
such as A,
B,
and C.
Straight lines, and especially segments, are often labelled with lower-case
Latin letters, such as a,
b,
and c,
but straight lines are sometimes also labelled as subscripted ells, such
as L_{1}
for "line one".

Corners of figures, such as the corners
of squares, are called "vertices" (VURR-tuh-seez); the singular
is "vertex" (VURR-teks).

If the meaning is clear, an angle
may be referred to by just the point at its vertex, such as ∠C
for the right angle show here:

Properly, angles should be named
completely, such as ∠BCA.

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If you're not sure that your meaning will
otherwise be clear, or if you're not sure which naming convention your
instructor prefers, use the three-letter method. That way, your meaning
will always be clear.

In triangles, angles and opposite sides
are usually corresponding upper- and lower-case Latin letters, as displayed
in the picture above. The angle at A is
opposite the side a,
the angle at B is
opposite the side b,
and so forth. If your book does not provide specifications of orientation,
such as a picture showing the labelled sides and angles or a worded description,
you should probably assume this same-letter, different-case oppositional
orientation.

To indicate the length of a line segment
AB,
you should use the absolute-value notation: |AB|
= 3 cm. But many texts omit this, using
AB
to refer to both the segment and its length. To indicate the measure (the
size) of an angle, you should use the m()
notation: m(∠BCA)
= 90°. But many texts omit this
notation, too.

Arrows on lines are used
to indicate that those lines are parallel.

If there is more than one pair of
parallel lines, additional arrow-heads will be used. So this picture
shows that p
is parallel to q
and r
is parallel to s.

Congruent angles (angles having the
same measure or angle size) are indicated with arcs.

If there is more than one
pair of congruent angles, additional arcs will be used. So this
picture shows that angle A
is congruent to angle X
and angle B
is congruent to angle Y.

Congruent segments (segments
or polygon sides having the same length) are indicated by tick-marks.
If there is more than one pair of congruent segments, additional
tick-marks will be used. So this picture shows that side AB
is congruent to side CD
and side DA
is congruent to side BC.

Other notation, such as for rays, arcs,
etc, is usually defined in the text. Unfortunately, as old as geometry
is, the notation does not seem, even today, to be entirely standardized.
So pay particular attention to how your book does things, so you can follow
along, but don't be surprised if your instructor does something else.

For trigonometric functions, powers are
indicated directly on the function names. For instance, "the square
of the sine of beta" is written as sin^{2}(β),
and this notation means [sin(β)]^{2}.
Multipliers on the variable go inside the argument: sin(2β)
does not mean the same thing as sin^{2}(β).
Some texts omit the function-notation parentheses,
writing sin^{2}β
and sin2β,
which can lead to confusion, especially when these expressions are hand-written.
Try to remember to use the parentheses, so you can be clear in your own
work. Also, try not to get in the lazy habit of omitting the arguments
of the functions, writing things like sin^{2}
+ cos^{2} = 1, as this
will lead to severe problems when the argument is not something
simple like just "x".

The final "convention" I'll mention
is really an assumption that you should remember not to make: Do
not assume that pictures are "to scale"!