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**Proving Segment Relationships**

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

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**If AB CD, and CD EF, then AB EF**

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 Reflexive Property AB AB Symmetric Property If AB CD, then CD AB Transitive Property If AB CD, and CD EF, then AB EF It's not what you look at that matters, it's what you see. Henry David Thoreau

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**Use paper to solve Given BC = DE Prove AB + DE = AC Statements Reasons**

AB + BC = AC AB + DE = AC Given Segment Addition Postulate Substitution

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**Use paper to solve Given PR QS Prove PQ RS Statements Reasons**

PQ + QR = PR QR + RS = QS PQ + QR = QR + RS PQ = RS PQ RS Given Definition of Congruence Segment Addition Postulate Substitution Subtraction

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**Proof with Segment Addition process**

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

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**Proof with Segment Addition process**

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

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**Proof with Segment Congruence process**

J Prove the following: Given: JK KL, HJ GH, KL HJ Prove: GH JK K L Statements Reasons H G JK KL, KL HJ JK HJ HJ GH JK GH GH JK Given Transitive Property Symmetric Property

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**Given: AC = AB AB = BX CY = XD Prove: AY = BD**

Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition Property AC + CY = BX + XD 4. AY = BD 6. Substitution 6. Proof: Statements Reasons 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, even

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Over Lesson 2–6 5-Minute Check 1 A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the property that.

Over Lesson 2–6 5-Minute Check 1 A.Distributive Property B.Addition Property C.Substitution Property D.Multiplication Property State the property that.

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