Warm Up Week 7 If I run, then you walk. 1) What is the contrapositive? 2) Place marks to show congruence: AB ≅ DE and BC ≅ EF : B A C E D F

Geometry 2.5 Day 1 I will justify statements about congruent segments. EqualCongruent Definition of Congruent Segments AB ≅ CD,AB = CD Rule 1 For proofs, change congruency to equality because you will work with numbers.

Ex 1 StepReason Given PQ = XY X P Q Y XY = PQ Given: XY ≅ PQ Prove: PQ ≅ XY XY ≅ PQ Definition of Congruent Segments Symmetric Property of Equality PQ ≅ XY Definition of Congruent Segments

StepReason R P Q Given: Q is the midpoint of PR Prove: PQ = ½PR and QR = ½PR Q is the midpoint of PR Given PQ = QR Definition of Midpoint PQ + QR = PR Segment Addition Postulate PQ + PQ = PR Substitution Property of Equality 2PQ = PRSimplify PQ = ½PR Division Property of Equality QR = ½PR Substitution Property of Equality Ex 2

StepReason, Given Transitive Property of Equality AB = CD Definition of Congruent Segments 9x – 13 = 2x + 8 Substitution Property of Equality 7x = 21 Addition Property of Equality x = 3 Division Property of Equality Ex 3 Given: AB ≅ BC, CD ≅ BC AB ≅ BC CD ≅ BC AB ≅ CD 7x – 13 = 8 Subtraction Property of Equality ABC D 9x x + 8

StepReason Ex 4 LK = 5Given JK = 5Given LK = JK Transitive Property of equality Definition of Congruent Segments Given: LK = 5, JK = 5, JK ≅ JL Prove: LK ≅ JL J K L LK ≅ JK JK ≅ JL Given LK ≅ JL Transitive Property of equality

Do: 1 Assignment: Handout - Given: AB = BC StepReason C A B Prove: AC = 2 AB

Do: 1 Assignment: Textbook Page 105, All and All What is the property : If AB ≅ CD, then CD ≅ AB