2.4: Special Pairs of Angles Page 50 Pre-AP Geometry 1

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

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

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.

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

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.

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.

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

2.5: Perpendicular Lines Page 56 Pre-AP Geometry 1

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

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.