Download Honors Geometry Section 1.3 part2 Special Angle Pairs

Geometry Section 1.6
Special Angle Pairs
Two angles are adjacent angles if
they have the same vertex and share a side in common.
1 and 2 or 2 and 3 or ...
Two angles are vertical angles if
they are the opposite angles formed when
two lines intersect. 1 and 3 or 2 and 4
While a postulate is
a statement accepted as true without proof
a theorem is a
a statement that can be proven.
Theorem 2.6: Vertical Angle
Theorem:
If two angles are vertical angles,
then they are congruent.
Complementary angles are two
angles whose measures have a
sum of 90 degrees.
Each angle is called a complement
__________
of the other.
Supplementary angles are two
angles whose measures have a
sum of 180 degrees.
Each angle is called a ___________
supplement
of the other.
Example 1: Complete the chart.
27
117
45
45
(90  x) (180  x)
3x  7  5x 18  180
8 x  25  180
8 x  155
mA  65.125
x  19.375
mB  114.875
Example 3: The measure of an angle is
10 less than three times the measure
of its complement. Find the measure
of both angles.
x  angle
90  x  compliment
180 - x  supplement
x  3(90  x)  10
x  270  3 x  10
4 x  260
x  65
65 & 25
A linear pair is two angles which share
a side in common and whose
noncommon sides form a straight line.
Linear Pair Postulate
If two angles form a linear pair, then
they are supplementary.
Example 4: Name all angles that
form a linear pair with BMA .
BMD
AME
3 x  6  2 x  5  180
5 x  1  180
5 x  181
x  36.2
2(36.2)  5  77.4
2x  5
5y
3x  6
5 y  77.4
y  15.48