Download Lesson 1.5 Notes - Dr. Dorena Rode

Geometry
Lesson 1.5 Angle Pair Relationships
Two angles are adjacent if they:
and
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1) have the same vertex
2) share a common side
3) have no interior points in common
Complementary angles are two angles that add up to 90 degrees.
4
1
3
2
adjacent complementary angles
nonadjacent complementary angles
Supplementary angles are two angles that add up to 180 degrees.
7
5
6
adjacent supplementary angles
8
nonadjacent supplementary angles
** Supplementary angles that form a line are called a linear pair. Angles 5 and 6 above are a linear pair.
Vertical angles are a pair of nonadjacent angles formed by two intersecting lines.
∠𝐴 and ∠𝐶 are vertical angles
B
A
∠𝐵 and ∠𝐷 are vertical angles
C
D
Vertical angles are congruent. This means their measures are equal.
∠𝐴 ≅ ∠𝐶 ∴ 𝑚∠𝐴 = 𝑚∠𝐶
∠𝐵 ≅ ∠𝐷 ∴ 𝑚∠𝐵 = 𝑚∠𝐷
Note: the symbol ∴ means “therefore”