Download Note Sheet 1-5

June 20, 2013
Geometry 1-5 Angle Relationships
Angles have many special relationships. We will look at a
few of these relationships today.
Two angles that lie in the same plane, share a common side
and a common vertex are called adjacent angles. Angles that
do not fit this discription are called nonadjacent angles.
1
2
Angles 1
and 2 are
adjacent.
Complementary angles are
two angles with measures
that add up to 90.
3 4
Angles 3 and 4
are nonadjacent.
Supplementary angles are
two angles with measures
that add up to 180.
Two special relationships to be aware of:
Vertical angles are congruent.
The angles in a linear pair are supplementary.
A linear pair of angles are
two adjacent angles whose
noncommon sides form a
straight line.
Vertical angles are
nonadjacent angles formed
by intersecting lines.
1
2
Angles 1 and 2
are a linear pair.
1
3 4 2
Angles 1 and 4 are vertical
angles; angles 2 and 3 are
vertical angles.
Find the measures of two supplementary angles if the
difference in their measures is 18.
x + y = 180
x - y = 18
2x = 198
x = 99
99 + y = 180
y = 81
The two angles are 99 and 81.
June 20, 2013
x + y = 90
x = 2y + 12
2y + 12 + y = 90
3y + 12 = 90
3y = 78
y = 26
Lines, segments, and/or rays which intersect at right angles
are called perpendicular . The symbol for this is .
T
Find the measures of two complementary angles if the larger
angle is 12 degrees more than twice the smaller angle.
T
PAUSE HERE AND TRY THIS ONE.
Find values for x and y so that PR SQ.
x + 26 = 90
x = 64
R 4y - 2
The two angles are 64 and 26.
Sometimes we can assume things from a diagram; other
times, we cannot make assumptions.
CAN ASSUME
Points that appear coplanar are coplanar.
Points that lie on a line togethre are collinear.
Lines that appear to intersect do intersect.
Points appear in the order shown.
Points that appear to be interior to an angle are interior;
those that appear to be exterior are exterior.
Angles that appear adjacent are adjacent; those that appear
to be a linear pair are a linear pair.
S
2x
P
5x + 6
Q
2x + 5x + 6 = 90
7x + 6 = 90
7x = 84
x = 12
4y - 2 = 90
4y = 92
y = 23
CANNOT ASSUME
We cannot assume lines are perpendicular.
We cannot assume segments are congruent.
We cannot assume angles are congruent.
We cannot assume relative sizes of angles or segments.