GEOMETRIC INSTRUMENTS
POINT
Definition: Specifies only
location; it has no
length, width, depth,
and has a dimension of
0.
The bottom bridge pin
represents a “point”
because it has a
location on where the
line starts (the guitar
string starts).
T
LINE
Definition: A line has only
one dimension: length. It
has no width and
continues in two
directions endlessly.
The bass string
represents a “line”
because it almost
continues endlessly in
both direction (one end
to the nut and one to
the bridge).
A
B
LINE SEGMENT
Definition: A line
segment is the portion
of a line lying strictly
between two points. It
has a limit of length and
no width.
The flute represents a
“line segment”
because it has a limit of
length with no width
and has an
endpoint(the crown)
that stops at another
point.
D
D
C
RAY
Definition: A ray can
be thought of as a half
a line. It has a point on
one end, and it
extends infinitely in the
other direction.
The string of the
ukulele represents a
“ray” because it has a
point on one end
(tuning peg) and a
line (string) that
extends infinitely in the
other direction.
F
F
E
E
OPPOSITE RAYS
Definition: Two rays with a
common endpoint that
point in opposite directions
and form a straight line.
The string on the Guzheng
(or Chinese Zither)
represents “opposite rays”
because the two rays (the
string in the middle that
extends outward) have a
common endpoint that
point in opposite
directions.
H
G
I
PARALLEL LINES
Definition: Parallel lines
are two lines equal
distance apart in the
same plane that never
intersect.
The nylon guitar strings
that are on a classical
guitar represent
“parallel lines” because
the two lines (strings) are
equal distance apart
that never intersect.
J
K
ACUTE ANGLE
Definition: An angle
that is less than 90
degrees.
The one side of the
triangle represents an
“acute angle”
because the triangle is
less than 90 degrees.
N
N
O
O
P
P
OBTUSE ANGLE
Definition: An angle
that is more than 90
degrees and less
than 180 degrees.
The lute represents
an “obtuse angle”
because the angle
at the head of the
lute to the neck is
less than 180
degrees and more
than 90 degrees.
Q
SS
R
RIGHT ANGLE
Definition: An angle that
is exactly 90 degrees.
T
The Theremin represents
a “right angle” because
the arm and antenna of
the Theremin are at an
angle that’s exactly 90
degrees.
U
V
VERTICAL ANGLES
Definition: A pair of equal
angles formed on opposite
sides of the point at which
two lines intersect.
The 4 neck guitar
represents vertical angles
because the pair of equal
angles are formed on
opposite sides of the point
at which two lines intersect
(at which the two guitars
intersect).
1
2
ADJACENT ANGLES
Definition: Two angles that
are formed by the
intersection of two straight
lines and lie on the same
side of one line.
The Great Drone and the
Tenor Drone represents
“adjacent angles”
because the two angles
that are formed by the
lines (drones) lie on the
same side of one line
(Tenor Drone).
3
4
INTERSECTING LINES THAT ARE NONPERPENDICULAR TO EACH OTHER
Definition: Two obtuse
angles or acute angles
formed on opposite sides
of the point at which two
lines intersect.
The mallets of the
xylophone represent
“intersecting lines that are
non-perpendicular to
each other” because the
two acute angles form
angles on opposite sides
of the point at which the
two lines intersect (mallets
intersect).
b
a
W
INTERSECTING PLANES
Definition: Two planes
that meet at a single
line.
The black and white
keys represent
“intersecting planes”
because the side of
the black key and
white key meet at
the line segment XY.
X
D
C
Y
COMPLEMENTARY ANGLES
Definition: Two acute
angles that add up to
give a right angle, 90°.
The vibraslap represents
“complementary
angles” because the
angle is at 90 degrees
and it has two acute
angles in it.
5
6
MIDPOINT OF LINE SEGMENT
Definition: The point that
is halfway between the
endpoints of the line
segment.
The master volume bar
on the Yamaha Motif 6
represents a “midpoint
of a line segment”
because the point is
halfway between the
line segment (slide
potentiometer).
Z
LINEAR PAIR
Definition: A pair of
adjacent angles that
make up a
supplementary angle on
a straight line.
The berimbau represents
a “linear pair” because
the angles lie on a
straight line that are
adjacent.
7
8