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2.6 Prove Statements About Segments and Angles

2.6 Prove Statements About Segments and Angles. Objectives. Write proofs involving segment and angle addition Write proofs involving segment and angle congruence. Two-Column Proof. Recall what a two-column proof was…

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2.6 Prove Statements About Segments and Angles

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  1. 2.6 Prove Statements About Segments and Angles

  2. Objectives • Write proofs involving segment and angle addition • Write proofs involving segment and angle congruence

  3. Two-Column Proof Recall what a two-column proof was… • Two-Column Proof – A proof format used in geometry in which an argument is presented with two columns, statementsand reasons, to prove conjectures and theorems are true. Also referred to as a formal proof.

  4. Proof: Statements Reasons Two-Column Proof

  5. Prove the following. Given: PR = QS Prove: PQ = RS Proof: Statements Reasons 1. 1. Given PR = QS 2. 2. Subtraction Property PR – QR = QS – QR 3. 3. Segment Addition Postulate PR – QR = PQ; QS – QR = RS 4. 4. Substitution PQ = RS Example 1:

  6. Prove the following. Given: Prove: Your Turn:

  7. Proof: Statements Reasons 1. 1. Given AC = AB, AB = BX 2. 2. Transitive Property AC = BX CY = XD 3. 3. Given 4. AC + CY = BX + XD 4. Addition Property 5. 5. Segment Addition Property AC + CY = AY; BX + XD = BD 6. 6. Substitution AY = BD Your Turn:

  8. Congruence of Segments Theorem 2.1 (Congruence of Segments) Congruence of segments is reflexive, symmetric, and transitive. Reflexive Property: AB AB Symmetric Property: If AB  CD, then CD  AB. Transitive Property: If AB  CD and CD  EF, then AB  EF.

  9. Congruence of Angles Theorem 2.2 (Congruence of Angles) Congruence of angles is reflexive, symmetric, and transitive. Reflexive Property:A  A Symmetric Property: If A  B , then B  A Transitive Property: If A  B and B  C , then A  C .

  10. Prove the following. Given: Prove: Example 2:

  11. Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. 3. Given 4. Transitive Property 4. 5. Transitive Property 5. Example 2:

  12. Prove the following. Given: Prove: Your Turn:

  13. Statements Reasons 1. 1. Given 2. 2. Transitive Property 3. 3. Given 4. 4. Transitive Property 5. 5. Symmetric Property Your Turn: Proof:

  14. Assignment • Geometry: Pg. 116 – 119 #3 – 13, 16, 21, 22

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