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. • QA = QA • If AB ≅ BC and BC ≅ CE then AB ≅ CE Reflexive property of equality Transitive property of congruence

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

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

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

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

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

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

2-7 Proving Segment Relationships