Proving things about Angles 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 H G 138° 42° P G and P are supplementary. H and P are supplementary. Thus, G H
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 60° M 30° N Q N and M are complementary. Q and M are complementary. Thus, N Q
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 mBHD = mCHE = mEHF = 90° If m3 = 42, then m6 = _____ 42 If mBHE = 142, then m1 = _____ 52 If m1 = 37, then m6 = _____ 37 If mEHG = 132, then m7 = _____ If m7 = 51, then m3 = _____ 39 If mEHB = 153, then m2 = _____ 27 1 2 3 4 5 6 7 • A • B • C • D • E • F H • G
Write a Two Column Proof Given: 1 and 2 are Supplementary 3 and 2 are Supplementary Prove: 1 3 Statements Reasons 1 and 2 are Supplementary 3 and 2 are Supplementary 1. Given 2. m1 + m2 = 180 m3 + m2 = 180 2. Def. Supp. Angles 3. m1 + m2 = m3 + m2 3. Substitution 4. m1 = m3 4. Subtraction 5. 1 3 5. Def. Congruent Angles
Given: 1 and 2 are complementary 1 3 and 2 4 Prove: 3 and 4 are complementary Statements Reasons 1. Given 1. 1 and 2 are complementary 1 3 and 2 4 2. m1 + m2 = 90 2. Def. of Complementary Angles 3. m1 = m3, m2 = m4 3. Def. Angles 4. m3 + m2 = 90 4. Substitution 5. m3 + m4 = 90 5. Substitution 6. 3 and 4 are complementary 6. Def. of Complementary Angles