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Chapter 2.7 Proving Segment Relationships Spi.1.4 Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems. Check.4.3 Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs Objective: Practice using proofs for geometric relationships by starting with segments

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Geometric Properties 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. Add to your listing It's not what you look at that matters, it's what you see. Henry David Thoreau Reflexive Property AB AB Symmetric Property If AB CD, then CD AB Transitive Property If AB CD, and CD EF, then AB EF A BC ABBC AC

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Use paper to solve Given BC = DE Prove AB + DE = AC Statements Reasons 1. Given 2. Segment Addition Postulate 3. Substitution 1. BC = DE 2. AB + BC = AC 3. AB + DE = AC

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Use paper to solve Given PR QS Prove PQ RS PQ SR Statements Reasons 1. Given 2. Definition of Congruence 3. Segment Addition Postulate 4. Segment Addition Postulate 5. Substitution 6. Subtraction 7. Definition of Congruence 1. PR QS 2. PR = QS 3. PQ + QR = PR 4. QR + RS = QS 5. PQ + QR = QR + RS 6. PQ = RS 7. PQ RS 8.

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Proof with Segment Addition process StatementsReasons 1. Given 2. Addition Property 3. Segment Addition Postulate 4. Substitution PQ SR Prove the following: Given: PQ = RS Prove: PR = QS 1. PQ = RS 2. PQ + QR = QR + RS 3. PQ + QR = PR and QR + RS = QS 4. PR = QS

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Proof with Segment Addition process StatementsReasons 1. Given 2. Subtraction Property 3. Segment Addition Postulate 4. Substitution PQ SR Prove the following: Given: PR = QS Prove: PQ = RS 1. PR = QS 2. PR - QR = QS - QR 3. PR - QR = PQ and QS - QR = RS 4. PQ = RS

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Proof with Segment Congruence process StatementsReasons 1. Given 2. Transitive Property 3. Given 4. Transitive Property 5. Symmetric Property J LK Prove the following: Given: JK KL, HJ GH, KL HJ Prove: GH JK 1. JK KL, KL HJ 2. JK HJ 3. HJ GH 4. JK GH 5. GH JK G H

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Prove the following. Given:AC = AB AB = BX CY = XD Prove:AY = BD 1. Given AC = AB, AB = BX Transitive Property AC = BX Given CY = XD Addition PropertyAC + CY = BX + XD4. AY = BD 6. Substitution6. Proof: StatementsReasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ? Segment Addition Postulate

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Practice Assignment Page 145, 4-16 even

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