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Chapter 2.7

Chapter 2.7. Proving Segment Relationships. Objective: Practice using proofs for geometric relationships by starting with segments. Geometric Properties . Add to your listing. Postulate 2.8 (Ruler Postulate)

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Chapter 2.7

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  1. Chapter 2.7 Proving Segment Relationships Objective: Practice using proofs for geometric relationships by starting with segments

  2. Geometric Properties Add to your listing • 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 zeros 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 or • If AB + BC = AC, then B is between A and C • Theorem 2.2 • Congruence of segments is reflexive, symmetric, and transitive. AB BC A B C AC It's not what you look at that matters, it's what you see. Henry David Thoreau

  3. Use paper to solve • Given BC = DE • Prove AB + DE = AC • Statements • Reasons • BC = DE • AB + BC = AC • AB + DE = AC • Given • Segment Addition Postulate • Substitution

  4. Use paper to solve P Q S R • Given PR  QS • Prove PQ  RS • Statements • Reasons • PR  QS • PR = QS • PQ + QR = PR • QR + RS = QS • PQ + QR = QR + RS • PQ = RS • PQ  RS Given Definition of Congruence Segment Addition Postulate Segment Addition Postulate Substitution Subtraction Definition of Congruence

  5. Proof with Segment Addition process Statements Reasons Given Addition Property Segment Addition Postulate Substitution PQ = RS PQ + QR = QR + RS PQ + QR = PR and QR + RS = QS PR = QS Prove the following: Given: PQ = RS Prove: PR = QS P Q S R

  6. Proof with Segment Addition process Statements Reasons Given Subtraction Property Segment Addition Postulate Substitution PR = QS PR - QR = QS - QR PR - QR = PQ and QS - QR = RS PQ = RS Prove the following: Given: PR = QS Prove: PQ = RS P Q S R

  7. Proof with Segment Congruence process Statements Reasons Given Transitive Property Given Transitive Property Symmetric Property JK  KL, KL HJ JK  HJ HJ  GH JK  GH GH  JK J Prove the following: Given: JK  KL, HJ GH, KL HJ Prove: GH  JK L K H G

  8. Prove the following. Which reason correctly completes the proof? Proof: Given:AC = ABAB = BXCY = XDProve:AY = BD 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. ________________ AC + CY = AY; BX + XD = BD 6. 6. Substitution AY = BD Segment Addition Postulate

  9. Practice Assignment • Page 145, 4-16 even

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