2 7 Proving Segment Relationships Ms Andrejko Real

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, TU≅LN SU =LR , TU=LN Prove: . . . T S L N U R 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+NRLN Subtraction Prop. ST = NR ST ≅ NR Substitution Property 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: Prove: LK ≅ NM, KJ ≅ MJ LK = NM, KJ = MJ LK + KJ = NM + MJ REASONS GIVEN Definition of congruent segments Add. Prop. LJ = LK+KJ, NJ=NM+MJ Segment addition post. LJ = NJ Substitution prop. LJ ≅ NJ Def. of congruent

Example: Fill in the proof Given: W X Y Z Prove: 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

Practice: Fill in the proof Given: X is the midpoint of S SY Z is the midpoint of YF XY = YZ STATEMENTS Prove: ZF midpoint ≅ SX X is the 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