Ms. Andrejko 2-7 Proving Segment Relationships

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 2. 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. 1. If Q is between P and R, then PR = PQ + QR. 2. 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:.... U.. S T L N R STATEMENTSREASONS SU ≅ LR, TU ≅ LN Definition of congruent segments SU = ST+ TU LR= LN+NR ST+TU = LN+NR ST+LN = LN+NR ST+LN-LN=LN+NR-LN Substitution Property ST ≅ NR GIVEN SU =LR, TU=LN Segment + post. Substitution Prop. Substitution prop. Subtraction Prop. ST = NR Def. of congruent

Practice STATEMENTSREASONS Given AB = CD CD = AB Definition of congruent segments AB ≅ CD Def. of congruent Symmetric CD ≅ AB

Practice- Complete the Proof Given: Prove: STATEMENTSREASONS LK ≅ NM, KJ ≅ MJ Definition of congruent segments LK + KJ = NM + MJ Segment addition post. LJ = NJ LJ ≅ NJ 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: Z X W Y STATEMENTSREASONS Given Def. of congruence XY = XY WX +XY = YZ +XY Segment addition post. Substitution Def. of Congruence 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 S X Y Z F STATEMENTSREASONS Given XY ≅ YZ Def. of Midpoint SX ≅ YZ Transitive Prop. ZF ≅ SX X is the midpoint of SY Z is the midpoint of YF XY = YZ SX ≅ XY ; YZ ≅ ZF Def. of Congruence Substitution SX ≅ ZF Symmetric