GEOMETRIC INSTRUMENTSGEOMETRIC 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). AB

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 C D

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. E F E F

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. K J

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 OP N OP

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. S Q R S

RIGHT ANGLE Definition: An angle that is exactly 90 degrees. The Theremin represents a “right angle” because the arm and antenna of the Theremin are at an angle that’s exactly 90 degrees. T 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). 12

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). 4 3

INTERSECTING LINES THAT ARE NON- PERPENDICULAR 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). a b 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. D C X 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. 6 5

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. 8 7