∠, the angle symbol
In geometry, an angle is the figure formed by two rays sharing
a common endpoint, called the vertex of the
angle. The magnitude of the angle is the "amount of rotation"
that separates the two rays, and can be measured by considering the length of
circular arc swept out when one ray is rotated about the vertex to coincide
with the other (see "Measuring angles", below). Where there is no
possibility of confusion, the term "angle" is used interchangeably
for both the geometric configuration itself and for its angular magnitude
(which is simply a numerical quantity).
http://en.wikipedia.org/wiki/Angle
Parallel
(geometry)
Parallelism is a term in geometry and in everyday life that
refers to a property in Euclidean space of two or more lines or planes, or a combination of these.
The existence and properties of parallel lines are the basis of Euclid's parallel
postulate. Two lines in
a plane that do not intersect or meet are called parallel lines.
The parallel symbol is 
. For example, 
indicates
that line AB is parallel to line CD.
As shown by the tick marks,
lines a and b are parallel. This can be proved
because the transversal t produces congruent
angles.
http://en.wikipedia.org/wiki/Parallel_(geometry)
Transversal line
In geometry,
a transversal line is a line that passes through two or more other coplanar lines at different points.
In Euclidean geometry if lines a and b are parallel, and line t intersects lines a and b,
then corresponding angles formed by line t and the parallel lines are congruent.
Theorems
Theorem 9 If a transversal intersects two parallel lines, then the
alternate interior angles are congruent. (Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Transversal_line
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.
(Our solved example in mathguru.com also uses the below concept.
This is our own explanation, it is not taken from Wikipedia.)
The sum of all the angles in a Triangle
is 180
(Angle Sum Property)