Geometry Organising is what you do before you do something, so that when you do it, it is not all mixed up. A.A. Milne Today: Over Proof Intro 2.5 Instruction Practice

2.5 Postulates and Proofs Objectives: 1. Justify statements about congruent segments. 2. Write reasons for steps in a proof. Vocabulary: Reflexive, Symmetric, Transitive

2.5 Postulates and Proofs Terminology of Geometry Theorem: A true statement that follows as a result of other true statements. Two-column proof: numbered statements and reasons that show the logical order of an argument.

2.5 Postulates and Proofs Given: HIJK is a rectangle Prove: HK = 6 6

2.5 Postulates and Proofs Properties of Equality: Segment Length Angle Measure Reflexive For any segment AB, For any angle A, AB = AB mA = mA Symmetric If AB = CD, then If mA = mB, CD = AB then, mB = mA Transitive If AB = CD and If mA = mB CD = EF then AB = EF and mB = mC, then mA = mC

2.5 Postulates and Proofs Now have same properties of congruence Reflexive: AB  AB A  A Symmetric: If AB  CD, If A  B, then CD  AB then B  A Transitive: If AB  CD and If A  B and CD  EF, then B  C, then AB  EF A  C

2.5 Postulates and Proofs statements reasons 1 Given: m1 = m2 and m3 = m4 Prove: m1 = m4 2 3 statements reasons 4

Geometry Organising is what you do before you do something, so that when you do it, it is not all mixed up. A.A. Milne Assignment: 2.5 p 131: 7, 9, 30 (set it up like in our notes, get as far as you can!), 52