Lesson 2 Understanding and Writing GEOMETRIC PROOF.pptx

Geometric Proof

1. GEOMETRIC PROOF LESSON 2

2. OBJECTIVE Write two-column geometric proofs.

3. Introduction to Geometric Proof When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them. Hypothesis Conclusion Definitions Postulates Properties Theorems A proof is a logical argument that establishes the truth of a statement. 

4. Introduction to Geometric Proof When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them. Hypothesis Conclusion Definitions Postulates Properties Theorems A proof is a logical argument that establishes the truth of a statement. 

5. Some Helpful Properties

6. A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of the conjecture. In a two-column proof , you list the steps of the proof in the left column. You write the matching reason for each step in the right column. Before you start writing a proof, you should plan out your logic. Sometimes you will be given a plan for a more challenging proof. This plan will detail the major steps of the proof for you.

7. If a diagram for a proof is not provided, draw your own and mark the given information on it. But do not mark the information in the Prove statement on it. Helpful Hint

8. The Structure of Geometric Proof

9. The Formal Proof of a Theorem ESSENTIAL PARTS OF THE FORMAL PROOF OF A THEOREM Statement: States the theorem to be proved. Drawing: Represents the hypothesis of the theorem. Given: Describes the Drawing according to the information found in the hypothesis of the theorem. Prove: Describes the Drawing according to the claim made in the conclusion of the theorem. Proof: Orders a list of claims (Statements) and justifications (Reasons), beginning with the Given and ending with the Prove; there must be a logical flow in this Proof.

10. Practice Write the letter of the correct justification next to each step. (Use one of them twice) A B C B

11. 2.6 Proof Statements 1. 2. 3. 4. Reasons 1. Given 2. 3. Substitution Prop. of = 4.

12. Proof Mark the diagram and answer the questions about the proof on the following slide. Statements Reasons

13. Additional Learning Resources http:// www.mathguide.com/lessons/GeometryProofs.html