7.2 SAT Math - Geometry Vocab

Know what the following things are and how they are noted:

Point

Point – A point is usually defined as "a location in space."  It has no dimension, measurement or mass.  It simply marks a spot that exists.  Points are usually shown as a dot on a line (•) and most often noted as capital letters, like A, P, O, etc.

Line Segment

Line segment – The space between two points.  A line segment is a short section of a line, which extends infinitely in both directions.  Any two points can make a line, though there are often many more points listed on a line.  A line is noted by two of the points that lie on that line, usually with a double-sided arrow above the letters, or by a single-lower case letter that is used to represent it:

So the line above could be called line m,  or even the reverse of those points .  If you were just being asked about the line segment, just a piece of that line, the line above the two points would not have arrows on it .  That means they're only talking about the portion between those two points, not the whole line.  With the arrows means they're talking about the whole line, even the parts that aren't shown.

Ray

Ray – A ray is line that only extends infinitely in one direction.  So it's like a line that comes to an end at a point, or a line segment that keeps going.  A ray is noted by a one-sided arrow and is usually referred to by either the point that starts it, or by that point and one other on the ray:

So the above ray could be called ray U, or .  On , there is also a line segment UV that is only the distance between U and V.

Plane

Plane – a plane is defined by three points in space.  Often, there will be more than three points on a plane, but it only needs three to be defined.  All the possible lines and points that lie on the same flat area in all directions exist on the plane.

When two rays converge at the same point, they create an angle.  An angle is notated by the symbol ∠ followed by three points, one from one ray, the vertex or place where the rays intersect, and a point from the other ray.  So the angle:

would be written as ∠DEF or ∠FED.  Sometimes they'll just refer to the angle by the vertex, such as ∠E.

Angels

Angles are measured in degrees, noted by the symbol °.  Sometimes, when discussing the measurement of an angle, they will write it as m∠DEF, such as m∠DEF = 35°.   A straight angle, which is really just a straight line, has a measure of 180°. 

Vertical angles occur when two lines cross to form four angles, like this:

Vertical angles are special because the angles opposite angles are equal.  That means ∠1 = ∠3 and ∠2 = ∠4.  Also, the adjacent angles add up to 180°.  That means ∠1 + ∠4 = 180° and ∠2 + ∠3 = 180°.

To bisect means to cut a line or angle exactly in half.

Perpendicular lines meet at a 90° angle and are noted by the symbol ⊥.

Parallel lines continue on forever next to each other without ever intersecting.  They are noted in a problem by two lines next to each other such as "line p||line m." 
-Trick to Watch Out For: Do not assume two lines are perpendicular unless told in the question by either the ⊥ symbol, a 90° angle, or a  in the corner indicating a 90° angle.  If a picture is NOT drawn to scale, never assume two lines are parallel unless told!

Parallel lines create a unique situation when cut by a transversal, which really just means a straight line that goes through both parallel lines.   In the picture below, lines r and s are parallel:

When this situation occurs, quite a few angles become equal to each other.  Let's say ∠1 has a measurement of 125°.  Angle 2, because it's on the straight line, must be 55°.  Angle 3 equals Angle 2, and Angle 4 equals Angle 1.  There's also a rule because of the parallel lines and the transversal that the top angles equal each other on the same side, so ∠1 = ∠5 and ∠2 = ∠6, and because ∠8 = ∠5 and ∠6= ∠7, if we know one angle's measurement in this situation, we know all of them.  If ∠1 = 125°, then ∠2 = 55°, ∠3 = 55°, ∠4 = 125°, ∠5 = 125°, ∠6 = 55°, ∠7 = 55°, and ∠8 = 125°.

An acute angle is an angle less than 90°, an obtuse angle is more than 90°, and a right angle equals 90°.  A 90° angle is most often marked by a small box in the corner where the two sides meet at 90°.

            -SAT Math Tip: Beware of right angles that are shown to you skewed, or not straight up and down.  Also, beware of mixing up the obtuse and acute angles.  Read carefully to establish which angle they given you information for, and which angle they're looking for.  For example:

If you were told that ∠ABC = 90°, you want to be sure to mark the angle marked B as 90°, even though it's upside down.  If you were given information for the second picture that allowed you to find the values of x and y, be sure to note which one the question is asking for.  It's a very common error to be asked for the obtuse angle, and for the student to answer the acute angle's measurement, which is always an option among the answer choices.

Two lines that are congruent, or equal in length, are noted as such by tick marks.   Two angles that are congruent are noted as such by a small arc in the corner of each angle as below:

Triangles and Trigonometry

• Similar triangles, congruent triangles, SOHCAHTOA and trig uses
• Tricks to Watch Out For and Hints
• Strategy: Size It Up and reminder to Put In Numbers

Triangles, Trigonometry
-special triangles (side relating and also 30-60-90, etc.), similar triangles, basic information (pythagorean theorem), congruent triangles
-SAT Math Tip: if you know trig well, use it, but usually special triangles is quicker and easier; three bases and three heights
-SAT Math Strategy: Guess at angles (eyeball) and don't forget to Throw in Numbers.