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2.5 Proving Statements about Segments and Angles

2.5 Proving Statements about Segments and Angles. Writing a Two Column Proof. Proof A logical argument that uses deductive reasoning to show that a statement is true Two-Column Proof Consists of numbered statements and corresponding reasons that show an argument in logical order

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2.5 Proving Statements about Segments and Angles

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  1. 2.5 Proving Statements about Segments and Angles

  2. Writing a Two Column Proof Proof • A logical argument that uses deductive reasoning to show that a statement is true Two-Column Proof • Consists of numbered statements and corresponding reasons that show an argument in logical order • Statement on the left is either given or a result of applying a known property or fact to statements already made • The reason on the right hand is the corresponding explanation to the statement

  3. Writing a Two-Column ProofExample 1 Write a two column proof for the situation below. Given: m<1 = m<3 Prove: m<DBA = m<EBC 1. m<1 = m<3 1. Given 2. m<DBA = m<3 + m<2 2. Angle Addition Postulate 3. m<DBA = m<1 + m<2 3. Substitution Property of Equality 4. m<1 + m<2 = m<EBC 4. Angle Addition Postulate 5. m<DBA = m<EBC 5. Transitive Property of Equality

  4. You try! Given Substitution Property of Equality 4x = 20 Division Property of Equality

  5. Using Properties of Congruence Theorem • A statement that can be proven

  6. Naming Properties of CongruenceExample 2

  7. Proving a Symmetric Property of CongruenceExample 3 Write a two column proof for the Symmetric Property of Segment Congruence.

  8. Writing a Two-Column ProofExample 4 2. Definition of a midpoint 3. AM = MB 3. Definition of congruent segments 4. AM + MB = AB 4. Segment Addition Postulate 5. AM + AM = AB 5. Substitution Property of Equality 6. 2AM = AB 6. Simplify 7. Division Property of Equality

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