1. Special Pairs of
Angles
Section 2-4

2. Three Kinds of “Special” Pairs
1. Complementary Angles (comp. ∠ ’s) – two angles
whose sum is 90 degrees.
D
60°
30°
E F
∠ D and ∠ F are complementary
∠ F is a complement of ∠ D

3. Three Kinds of “Special” Pairs
2. Supplementary Angles (supp. ∠ ’s) – two angles
whose sum is 180 degrees.
100° 80°
X Z
∠ X and ∠ Z are supplementary
∠ X is a supplement of ∠ Z

4. So, what’s the difference between a linear
pair and supplementary angles?

5. Three Kinds of “Special” Pairs
3. Vertical Angles (vert. ∠ ’s) – two nonadjacent angles
formed by two intersecting lines
2
1 3
4
∠ 1 and ∠ 3 are vertical angles
∠ 2 and ∠ 4 are vertical angles

6. And One New Theorem
Vertical Angle Theorem (VAT) – Vertical angles
are congruent.
P• •L
∠ POL ≅ ∠ KOJ
O
J •K ∠ JOP ≅ ∠ LOK
•

7. Complete with always, sometimes, or never
1. Vertical angles ____________ have a common vertex.
2. Two right angles are ____________ complementary.
3. Right angles are ____________ vertical angles.
4. Angles 1, 2, and 3 are ____________ complementary.
5. Vertical angles ____________ have a common supplement.