1. 2.4: Special Pairs of Angles
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Pre-AP Geometry 1

2. Angle Pair Relationships
Complementary Angles
Two angles that have a sum of 90º
Each angle is a complement of the other.
Non-adjacent complementary Adjacent angles complementary angles

3. Angle Pair Relationships
Supplementary Angles
Two angles that have a sum of 180º
Each angle is a supplement of the other.

4. Angle Pair Relationships
Example 1
Given that G is a supplement of H and mG is 82°, find mH.
Given that U is a complement of V, and mU is 73°, find mV.

5. Angle Pair Relationships
Example 2
T and S are supplementary.
The measure of T is half the measure of S. Find mS.

6. Angle Pair Relationships
Example 3
D and E are complements and D and F are supplements. If mE is four times mD, find the measure of each of the three angles.

7. Theorem 2-3 Vertical angles are congruent
Given: angle 1 and angle 2 are vertical angles
Prove∠1≅ ∠2 3 2 1
Statement
Reasons 1. 2. 3. 4.

8. Angle pair relationships
Find x and the measure of each angle. ∠A
32°
2x + 10

9. 2.5: Perpendicular Lines
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Pre-AP Geometry 1

10. Perpendicular lines Two lines that intersect to form right angles
We use the symbol ⊥ to show that lines are perpendicular. Line AB ⊥ Line CD C A B D

11. Perpendicular lines theorems
Theorem 2-4: If two lines are perpendicular, then they form congruent adjacent angles
Theorem 2-5: If two lines form congruent adjacent angles, then the lines are perpendicular
Theorem 2-6: If the exterior sides of two adjacent angles are perpendicular, then the angles are complementary.