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Lesson 2-7

Lesson 2-7. Proving Segment Relationships. Transparency 2-7. 5-Minute Check on Lesson 2-6. State the property that justifies each statement. 1. 2 (LM + NO) = 2 LM + 2 NO 2. If m  R = m  S , then m  R + m  T = m  S + m  T. 3. If 2 PQ = OQ , then PQ = ½ OQ.

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Lesson 2-7

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  1. Lesson 2-7 Proving Segment Relationships

  2. Transparency 2-7 5-Minute Check on Lesson 2-6 State the property that justifies each statement. 1. 2(LM + NO) = 2LM + 2NO 2. If mR = mS, then mR + mT = mS + mT. 3. If 2PQ = OQ, then PQ = ½OQ. 4. mZ = mZ 5. If BC = CD and CD = EF, then BC = EF. 6. Which property justifies the statement if 90 = mI, then mI = 90? Standardized Test Practice: A Substitution Property Reflexive Property B C Symmetric Property D Transitive Property

  3. Transparency 2-7 5-Minute Check on Lesson 2-6 State the property that justifies each statement. 1. 2(LM + NO) = 2LM + 2NO Distributive Property 2. If mR = mS, then mR + mT = mS + mT. Addition Property 3. If 2PQ = OQ, then PQ = ½OQ. Division Property 4. mZ = mZ Reflexive Property 5. If BC = CD and CD = EF, then BC = EF. Transitive Property 6. Which property justifies the statement if 90 = mI, then mI = 90? Standardized Test Practice: A Substitution Property Reflexive Property B C Symmetric Property D Transitive Property

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

  5. Vocabulary • No new vocabulary

  6. 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 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. Postulate 2.9, Segment Addition Postulate: If B is between A and C, then AB + BC = AC and if AB + BC = AC, then B is between A and C.

  7. Segment Proof ABC Given: ACDE; BCEFProve: ACDF DEF

  8. 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 Prove the following. Given: PR = QS Prove: PQ = RS

  9. 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 Prove the following. Given: AC = AB; AB = BX; CY = XD Prove: AY = BD

  10. Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. 3. Given 4. Transitive Property 4. 5. Transitive Property 5. Prove the following. __ __ __ ___Given: WX = YZ; YZXZ; XZWY Prove: WXWY

  11. Statements Reasons 1. 1. Given 2. 2. Transitive Property 3. 3. Given 4. 4. Transitive Property 5. 5. Symmetric Property Prove the following. __ ____ __ __ __Given: GDBC; BCFH; FHAE Prove: AEGD Proof:

  12. Summary & Homework • Summary: • Use properties of equality and congruence to write proofs involving segments • Homework: • pg 104-5: 12-18, 21, 23

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