Chapter 2 Section 2.6-Part 2

1. Chapter 2Section 2.6-Part 2 Proving things about Angles

2. Properties of Angle Congruence • Angle congruence is reflexive, symmetric, and transitive Reflexive: Symmetric: Transitive:

3. A B More Theorems and Postulates • Theorem 2.3 Right Angle Congruence Theorem • All right angles are congruent A and B are both right angles. Thus, A  B

4. 138° P H G 42° More Theorems and Postulates • Theorem 2.4 Congruent supplements theorem • If two angles are supplementary to the same angle, then they are congruent to each other G and P are supplementary. H and P are supplementary. Thus, G  H

5. Q 60° 30° N M More Theorems and Postulates • Theorem 2.5Congruent complements theorem • If two angles are complementary to the same angle, then they are congruent to each other N and M are complementary. Q and M are complementary. Thus, N  Q

6. More Theorems and Postulates • Postulate 12Linear Pair Postulate • If two angles form a linear pair, then they are supplementary • Theorem 2.6Vertical Angle Theorem • Vertical Angles are congruent

7. • A • B • G • F • C 2 3 4 1 H 7 5 • D 6 • E Complete the statement given that mBHD = mCHE = mEHF = 90° • If m3 = 42, then m6 = _____ • If mBHE = 142, then m1 = _____ • If m1 = 37, then m6 = _____ • If mEHG = 132, then m7 = _____ • If m7 = 51, then m3 = _____ • If mEHB = 153, then m2 = _____

8. Statements Reasons Write a Two Column Proof Given: 1 and 2 are Supplementary 3 and 2 are Supplementary Prove:1  3 • 1 and 2 are Supplementary • 3 and 2 are Supplementary 2. m1 + m2 = 180 m3 + m2 = 180 3. m1 + m2 = m3 + m2 4. m1 = m3 5. 1  3

9. 3 2 1 4 Statements Reasons Given: 1 and 2 are complementary 1  3 and 2  4 Prove: 3 and 4 are complementary 1. 1 and 2 are complementary 1  3 and 2  4 2. m1 + m2 = 90 3. m1 = m3, m2 = m4 4. m3 + m2 = 90 5. m3 + m4 = 90 6. 3 and 4 are complementary