Download Geometry Section 1.6 NMV Special Angle Pairs Two angles are

Geometry Section 1.6 NMV
Special Angle Pairs
Two angles are adjacent angles if __they have the same vertex and share a side in common
Name all adjacent angles in the diagram:
4
1
2
3
Two angles are vertical angles if ___they are the nonadjacent angle formed when 2 lines
intersect______
Name all the vertical angles in the diagram:
While a postulate is a statement without proof a theorem is a statement which can be proven.
Theorem 2.6: Vertical Angle Theorem: vertical angles are congruent.
State which angles are congruent based on the Vertical Angle Theorem:
*Complementary angles are two angles whose sum is equal to 90 degrees.
Each angle is called a complement of the other.
*Supplementary angles are two angles whose sum is equal to 180 degrees.
Each angle is called a supplement of the other.
Example 1: Complete the chart.
Angle Complement Supplement
63
135
x
Example 2: mA  3x  7 and mB  5x  18 . If  A and  B are supplementary, find the measure of
each angle.
Example 3: The measure of an angle is 10 less than three times the measure of its complement. Find the
measure of both angles.
Special Angle Pairs Notes NMV page 2
A linear pair is two angles that are adjacent and the non-common sides form a straight line
Linear Pair Postulate: If two angles form a linear pair, then they are supplementary
Use the figure at the right for examples 4 & 5.
Example 4: Name all angles that form a linear pair with BMA .
D
C
B
E
M
A
Example 5: If mAME  3x  6 , mDME  2x  5 , and
mBMA  5 y , find x and y.
D
C
B
M
A
E