Alternate and correspond-
ing angles—A pair of angles
that lie on opposite sides and
opposite ends of a transversal
(a line that cuts two or more
lines in the same plane) are
called alternate angles; both
these angles are equal if the
lines cut by the transversal are
parallel. They are also broken
into alternate interior angles
(the “inside” angles) and alter-
nate exterior angles (the “out-
side” angles). For two parallel
lines, the alternate interior
and exterior angles are
equal—or congruent. Corre-
sponding angles are pairs of
angles that lie on the same
sides and ends of a transversal.
Dihedral angle—A dihe-
dral (meaning “two bases”)
angle is one of the four angles
formed where two non-paral-
lel planes meet.
Complementary angles—
Two angles that add up to a
right angle are complemen-
tary. For example, the two
acute angles in a right trian-
gle are always considered
complementary, as their sum
adds up to 90 degrees of the
right triangle.
Supplementary angles—Two angles that add up to a straight angle (180 degrees)
are supplementary. If the angles are both supplementary to the same angle, then the
two angles are congruent.
What are perpendicular, orthogonal, normal,and tangent lines?
Lines are also classified by their relationship to other angles and lines. Perpendicular
linesare two lines, segments, or rays that intersect to form a right (90 degree) angle. 175
GEOMETRY AND TRIGONOMETRY
Among the types of angles are: 1. adjacent angles; 2. vertical (con-
gruent) angles; and 3. exterior and interior angles. In illustration 4
we see alternate interior angles (a 1 and a 2 ), alternate exterior
angles (b 1 and b 2 ), and corresponding angles (b 1 and c 1 ).