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Unit 3
Prior Vocabulary
Gallery
Adjacent Angles
Angles in the same plane that have a common
vertex and a common side, but no common
interior points.
In the figure above, angle FKI and angle FKH
are adjacent angles.
Transversal
A line that crosses two or more lines.
Alternate Interior Angles
Pairs of angles formed when a third line
(transversal) crosses two other lines and are
on opposite sides of the transversal and are
in between the other two lines.
Angles 1,2,3, and 4 are
interior angles. Angles 1
and 4 are alternate interior
angles. Angles 2 and 3 are
also alternate interior angles.
Line t (in red) is called a
transversal, a line crossing
two or more lines.
Same-Side Interior Angles
Pairs of angles formed when a transversal
(a third line) crosses two other lines.
These angles are on the same side of the
transversal and are outside the other two
lines.
Angles 1 and 3 are
same-side interior angles
and
angles 2 and 4 are
same-side
interior angles.
Alternate Exterior Angles:
Pairs of angles formed when a transversal
Crosses two other lines and are on opposite
sides of the transversal and are Outside the other
two lines.
Angles 1, 2, 3, and 4 are
all exterior angles.
Angles 1 and 4 are
alternate exterior angles.
Angles 2 and 3 are also
alternate exterior angles.
Line t (in red) is called a transversal, a line
Crossing two or more lines.
Complementary Angles
Two angles whose sum is 90º.
In the example to the right,
notice that at all times, angle
BAT + angle CAT = 90º.The
diagram to the left is the
typical representation of
complementary angle, but the
angles do not have to be
adjacent (as shown here) to
be complementary.
Congruent
Having the same size, shape and measure.
Notice that each figure below is congruent
to one other figure in the given set of
figures. The congruent pairs are congruent
because they have the same size and
shape, regardless of their orientation (the
way they are "sitting").
Corresponding Angles
Angles that have the same relative positions
in geometric figures.
For example, in the figure below there are two
triangles: a larger triangle, ABC, and a smaller
triangle, ADE. Angles ADE and ABC are
corresponding because they
both lie in the same relative
position in the two triangles.
Angles ABC and AED are
not corresponding since
they do not lie in the same
Relative position in the two triangles.
Equiangular
The property of a polygon whose angles are
all congruent.
For example, an equilateral triangle is
equiangular since its interior angles are equal
(to 60 degrees). In general, all regular polygons
such as equilateral triangle, square, pentagon,
and hexagon are equiangular.
Equilateral
The property of a polygon whose sides
are all congruent.
Regular Polygon
A polygon that is both equilateral and
equiangular.
Intersecting Lines
Two lines in a plane that cross each
other.
Two distinct lines intersect if they do not
have the same slope. In other words, if
the slopes are same (i.e., lines are
parallel), they do not intersect each other.
Linear Pair
Adjacent, supplementary angles. A linear
pair forms a straight line.
Remember that, by definition,
segment AC is part of a
straight line. Angles ABG and
CBG are adjacent angles
(since they share side BG).
The other side of each angle,
sides AB and BC,
form the line segment AC.
Therefore; we can call angles
ABG and CBG a linear pair.
Parallel Lines
Two lines that lie in the same plane and
they do not intersect.
Two lines that lie in the
Same plane and they do
not intersect. In the
following example, the
two red lines (k and l) are
parallel lines. Parallel lines
Are written using the
symbol | |. In this case k | | l.
Perpendicular Lines
Two lines that intersect at a right angle.
Skew Lines
Two lines that do not lie in the same
plane and never intersect and are not
parallel.
Supplementary Angles
Two angles whose sum is 180.
Notice that since angle ABC is
a straight angle, meaning that
its measure is 180 degrees,
then angle ABG + angle CBG
= 180 degrees. Therefore, we
can say that angles ABG and
CBG are supplementary.
Vertical Angles
Two nonadjacent angles formed by intersecting
lines or segments. Also called opposite angles.
In the above example, angles
EKG and HKF are opposite
angles because their sides are
formed by two intersecting
segments (EF & GH). Notice
that the angles have only one
point in common, the vertex
(K).