Lines and Angles Vocabulary

 

Angles are measured in degrees.  A circle has 360 degress, and of course half of a circle is 180 degrees.

Rays
Ray You can think of a ray as a laser beam.  It begins at one point and continues in one direction.   Two letters are needed to name a ray; one is the point where it begins and the other is any point that it goes through.  The symbol is the two letters with an arrow on top (as shown in diagram). Notice that RAY AB IS NOT THE SAME RAY BA. (rab.gif (860 bytes) is not rba.gif (860 bytes)).
Naming a Ray RAY rab.gif (860 bytes), consists of the points on segment sab.gif (864 bytes) and all points C on ab.gif (878 bytes) such that B is between A and C.  You can think of a ray as a segment that is extended indefinitely in one direction.  Rays have exactly one endpoint and that point is always named first when naming the ray. 

OPPOSITE RAY - Any given point on a line determines exactly two rays, called opposite rays.  This point is the common endpoint of the opposite rays.  In the figure below ray PS and ray PQ are opposite rays, and P is the common endpoint.

Opposite Rays

Angles:
Angle

ANGLE - An angle is formed by two rays which begin at the same point (if the two rays lie on the same line, then it is called a straight angle).  

There are several ways of naming angles: a capital letter at its vertex (Angle P); a small letter within the angle; a number within the angle, or by three captial letters, the middle letter is the vertex, the other two are points on each ray (Angle SPQ or angsym.gif (822 bytes) QPS).  We will often name angles by this last approach.

SIDES OF THE ANGLE - The two rays that form the angle are called the sides of the angle.  (Side PS & Side PQ)

 

  VERTEX - The common point for both rays is called the Vertex.  (Point P)

Interior & Exterior Regions

 

EXTERIOR & INTERIORS OF ANGLES - An angle separates a plane into THREE distinct regions, the interior of the angle, the exterior of the angle, and the angle itself.  (The Blue is the interior angle, and the Yellow is the exterior angle.)
Angle Addition Postulate

If R is in the interior of angsym.gif (822 bytes) PQS, then angsym.gif (822 bytes) PQR + angsym.gif (822 bytes) RQS = angsym.gif (822 bytes) PQS.
If angsym.gif (822 bytes) PQR + angsym.gif (822 bytes) RQS = angsym.gif (822 bytes) PQS, then R is in the interior of angsym.gif (822 bytes) PQS.

Angle Addition Postulate

Acute Angles
Acute Angle
An ACUTE ANGLE is one whose measure is LESS THAN 90 DEGREES. Notice angsym.gif (822 bytes) CAB does not quite reach 90 degrees... acute angles are always less than 90 degrees.
Right Angles
Right Angle
A RIGHT ANGLE is an angle whose measure is EXACTLY 90 DEGRRES. Right angles are denoted by a small square in its interior.
Obtuse Angles
Obtuse Angles
An OBTUSE ANGLE is one whose measure is GREATER THAN 90 AND LESS THAN 180 DEGREES. (This is a bit different definition from the book - this one is correct)
Straight Angles
Straight Angle
A STRAIGHT ANGLE is one whose measure is EXACTLY 180 DEGREES.  A straight angle is made up of two opposite rays.   Another important fact is that a straight angle forms a straight line.  This information will be used very frequently throughout the year.
Reflex Angle
Reflex Angle
A REFLEX ANGLE is one whose measure is GREATER THAN 180 AND LESS THAN 360 DEGREES.
Congruent Angle
Congruent Angles
CONGRUENT ANGLES - Two angles that have the same measure are called Congruent Angles.  Equal measure angles are labeled as shown in the diagram.
 
Adjacent Angles
Adjacent Angles ADJACENT ANGLES are angles in the same plane, that have a common vertex and a common side, but no common interior points.   In the diagram angsym.gif (822 bytes) HKF and angsym.gif (822 bytes) FKI share vertex K and side KF.
 
Vertical Angles
Vertical Angles VERTICAL ANGLES are two nonadjacent angles formed by two intersecting lines. (These can be found by the X that the two intersecting lines form)
 
Linear Pair
Linear Pair A LINEAR PAIR of angles are adjacent angles who non common sides are oppposite rays.  The sum of the measures of the angles in a linear pair is 180.
 
Supplementary Angles
Supplementary Angles SUPPLEMENTARY ANGLES - If the sum of the measures of two angles is 180 degrees, then the angles are supplementary.  (One angle is the supplement of the other.)

So you ask how is this different from a linear pair, well a linear pair must be adjacent angles whereas supplementary angles do not have to be, although they often are as in the diagram to the left.

 
Complementary Angles
Complementary Angles COMPLEMENTARY ANGLES - If the sum of the measures of two angles is 90 degrees, then the angles are complementary.  (One angle is the complement of the other.)
Perpendicular Lines
Perpendicular Lines PERPENDICULAR LINES are two lines that intersect to form a right angle.  Notice the square box at the intersecting angle - this represents the right angle that was formed.  Two diagrams have been provided.  The symbol used for perpendicular lines is an upside down T, perp.gif (834 bytes).  In our diagram we could say that line m perp.gif (834 bytes) line k.   Perpendicular lines intersect to form 4 right angles.
Perpendicular Angles