1 / 12

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.

mcesar
Download Presentation

Lesson 2-7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related