Chapter 2 Section 2 6 Part 2 Proving
- Slides: 9
Chapter 2 Section 2. 6 -Part 2 Proving things about Angles
Properties of Angle Congruence • Angle congruence is reflexive, symmetric, and transitive Reflexive: Symmetric: Transitive:
More Theorems and Postulates • Theorem 2. 3 Right Angle Congruence Theorem – All right angles are congruent A B A and B are both right angles. Thus, A B
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 138° H G and P are supplementary. H and P are supplementary. Thus, G H G P 42°
More Theorems and Postulates • Theorem 2. 5 Congruent complements theorem – If two angles are complementary to the same angle, then they are congruent to each other Q N 30° N and M are complementary. Q and M are complementary. Thus, N Q 60° M
More Theorems and Postulates • Postulate 12 Linear Pair Postulate – If two angles form a linear pair, then they are supplementary • Theorem 2. 6 Vertical Angle Theorem – Vertical Angles are congruent
Complete the statement given that m BHD = m CHE = m EHF = 90° • If m 3 = 42, then m 6 = _____ • 42 • If m BHE = 142, then m 1 = _____ • A • B • 52 • If m 1 = 37, then m 6 = _____ • 37 • If m EHG = 132, then m 7 = _____ • 42 • If m 7 = 51, then m 3 = _____ • 39 • If m EHB = 153, then m 2 = _____ • 27 2 3 4 1 • 7 C 6 • D • G 5 • E • F H
Write a Two Column Proof Given: 1 and 2 are Supplementary 3 and 2 are Supplementary Prove: 1 3 Statements Reasons 1. 1 and 2 are Supplementary 1. Given 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 2. Def. Supp. Angles 4. m 1 = m 3 4. Subtraction 5. 1 3 5. Def. Congruent Angles 3. Substitution
Given: 1 and 2 are complementary 1 3 and 2 4 Prove: 3 and 4 are complementary 2 1 3 4 Statements Reasons 1. 1 and 2 are complementary 1. Given 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 2. Def. of Complementary Angles 3. Def. Angles 4. Substitution 5. Substitution 6. Def. of Complementary Angles