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2-7 Proving Segment Relationships

2-7 Proving Segment Relationships. Ms. Andrejko. Real World. Postulates/Theorems. Ruler postulate Segment addition postulate Reflexive property Symmetric property Transitive property. Examples. Justify each statement with a property of equality, a property of congruence, or a postulate.

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2-7 Proving Segment Relationships

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  1. 2-7 Proving Segment Relationships Ms. Andrejko

  2. Real World

  3. Postulates/Theorems • Ruler postulate • Segment addition postulate • Reflexive property • Symmetric property • Transitive property

  4. Examples • Justify each statement with a property of equality, a property of congruence, or a postulate. • QA = QA • If AB ≅ BC and BC ≅ CE then AB ≅ CE Reflexive property of equality Transitive property of congruence

  5. Examples • Justify each statement with a property of equality, a property of congruence, or a postulate. • If Q is between P and R, then PR = PQ + QR. • If AB + BC = EF + FG and AB + BC = AC, then EF + FG = AC Segment addition postulate Transitive property of equality

  6. Example- Complete the Proof Given: Prove: GIVEN SU =LR , TU=LN . . . Segment + post. . . . U T S Substitution Prop. N L R Substitution prop. Subtraction Prop. ST = NR Def. of congruent

  7. Practice AB ≅ CD Def. of congruent Symmetric CD ≅ AB

  8. Practice- Complete the Proof Given: Prove: GIVEN LK = NM, KJ = MJ Add. Prop. LJ = LK+KJ, NJ=NM+MJ Substitution prop. Def. of congruent

  9. Example: Fill in the proof Given: Prove: Y W X Z WX ≅ YZ WX = YZ Reflexive Prop. Additive Prop. WY= WX+XY XZ = YZ+XY WY = XZ WY ≅ XZ

  10. Practice: Fill in the proof Given: X is the midpoint of SY Z is the midpoint of YF XY = YZ Prove: ZF ≅ SX F S X Z X is the midpoint of SY Z is the midpoint of YF XY = YZ Y Def. of Congruence SX≅ XY ; YZ ≅ ZF Substitution SX ≅ ZF Symmetric

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