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2.7 Proving Segment Relationships

2.7 Proving Segment Relationships. Objectives. Write proofs involving segment addition Write proofs involving segment congruence. Ruler Postulate. Postulate 2.8 ( Ruler Postulate )

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2.7 Proving Segment Relationships

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  1. 2.7 Proving Segment Relationships

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

  3. Ruler Postulate Postulate 2.8 (Ruler Postulate) The points on any line or line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number.  Basically, all segments have a measure.

  4. Segment Addition Postulate Postulate 2.9 (Segment Addition Postulate) If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C. AB BC A B C AC

  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. Segment Congruence Theorem 2.2 (Segment Congruence) 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. Prove the following. Given: Prove: Example 2:

  10. 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:

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

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

  13. Assignment • Geometry: Pg. 103 – 106 #4 – 7, 12 – 18, 21 • Pre-AP Geometry: Pg. 104 – 106 #12 – 23

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