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Building a System of Geometry Knowledge: Proof Strategies and Reasoning Techniques

This resource focuses on developing a systematic approach to geometric proofs. It begins with identifying properties and relationships between angles and segments, demonstrating how to justify conclusions using logical reasoning. The guide includes examples where given information leads to necessary conclusions, emphasizing the importance of diagrams and assumptions. It provides tools for constructing rigorous proofs, particularly in contexts such as bisecting segments and comparing angles. This worksheet aims to enhance understanding of geometric concepts and build a strong foundation in proof formulation.

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Building a System of Geometry Knowledge: Proof Strategies and Reasoning Techniques

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  1. Warm up Identify the Property 1. AB  CD given CD  AB __________________ 2. AB = CD given AB + BC = CD + BC __________________ 3. B  C and C  D given B  D __________________

  2. Plan of reasoning to complete geometric proofs What is given, what can be assumed from the diagram? What conclusions can be made from each given statement? What reason can you give to justify each conclusion? What order can you prove these conclusions? e) How can you arrive at what you are asked to prove? 2.4 Building a System of Geometry Knowledge Section 2-4 continued Proofs

  3. 5. Given: PQ bisects AB at point R and AR  RQ Prove: RB  RQ 2.4 Building a System of Geometry Knowledge Proof Q A R B P

  4. Statements Reasons 2.4 Building a System of Geometry Knowledge Proof

  5. 2.4 Building a System of Geometry Knowledge Given: m5 = m 8 and m6 = m7Prove: mABC = mEFG 6 7 5 8

  6. Statements Reasons 2.4 Building a System of Geometry Knowledge

  7. Intro to Proof Worksheet 2.4 Building a System of Geometry Knowledge assignment

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