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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. 1. QA = QA Reflexive property of equality 2. If AB ≅ BC and BC ≅ CE then AB ≅ CE Transitive property of congruence Examples Justify each statement with a property of equality, a property of congruence, or a postulate. 1. If Q is between P and R, then PR = PQ + QR. Segment addition postulate 2. If AB + BC = EF + FG and AB + BC = AC, then EF + FG = AC Transitive property of equality Example- Complete the Proof STATEMENTS Given: SU LR SU≅LR, TU≅LN TU LN Prove: ST NR .. . . .. S L T N U R SU =LR , TU=LN SU = ST+ TU LR= LN+NR REASONS GIVEN Definition of congruent segments Segment + post. ST+TU = LN+NR Substitution Prop. ST+LN = LN+NR Substitution prop. ST+LN-LN=LN+NR-LN Subtraction Prop. ST = NR Substitution Property ST ≅ NR Def. of congruent Practice STATEMENTS AB ≅ CD AB = CD CD = AB CD ≅ AB REASONS Given Def. of congruent Symmetric Definition of congruent segments Practice- Complete the Proof STATEMENTS Given: LK NM KJ MJ Prove: LJ NJ LK ≅ NM, KJ ≅ MJ LK = NM, KJ = MJ LK + KJ = NM + MJ LJ = LK+KJ, NJ=NM+MJ REASONS GIVEN Definition of congruent segments Add. Prop. Segment addition post. LJ = NJ Substitution prop. LJ ≅ NJ Def. of congruent Example: Fill in the proof Given: WX YZ W Y X Prove: WY XZ STATEMENTS WX ≅YZ WX = YZ XY = XY WX +XY = YZ +XY WY= WX+XY XZ = YZ+XY WY = XZ WY ≅ XZ REASONS Given Def. of congruence Reflexive Prop. Additive Prop. Segment addition post. Substitution Def. of Congruence Z Practice: Fill in the proof Given: X is the midpoint of SY S Z is the midpoint of YF XY = YZ Prove: ZF ≅ SX STATEMENTS X is the midpoint of SY Z is the midpoint of YF XY = YZ XY ≅YZ SX≅ XY ; YZ ≅ ZF SX ≅YZ SX ≅ ZF ZF ≅ SX F X Z Y REASONS Given Def. of Congruence Def. of Midpoint Substitution Transitive Prop. Symmetric