2.6 Geometric Proof2.6 Geometric Proof

Objectives: Write two-column proofs.Prove geometric theorems by using deductive reasoning.

Vocabulary:Theorem – a statement that can be proven true.Two-column proof – format for proofs where the statements are listed on the left and the reasons are listed on the right.

2.6 Geometric Proof2.6 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

2.6 Theorems2.6 Theorems

2.6 Theorems2.6 Theorems

2.6 Writing a Proof2.6 Writing a ProofA 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.

2.6 Tips2.6 Tips

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

2.6 Practice2.6 PracticeWrite the letter of the correct justification next to each step. (Use one of them twice)

A

B

CB

2.6 Proof2.6 Proof

Statements1.

2.

3.

4.

Reasons1. Given

2.

3. Substitution Prop. of =

4.

2.6 Proof2.6 ProofMark the diagram and answer the questions about the proof on Mark the diagram and answer the questions about the proof on the following slide.the following slide.

Statements Reasons

2.6 Proof Questions 2.6 Proof Questions 1. What was the given information?

2. What should be marked in the diagram?

3. What was the conjecture to be proved?

4. What titles should be put above the two columns?

2.6 Video explanation for 2.6 Video explanation for ProofsProofsCopy the link below and paste it into the address bar to visit the website. Watch the video explanations for the sample proof problems.

Link to Holt textbook video lessons:http://my.hrw.com/math06_07/nsmedia/homework_help/geo/geo_ch02_06_homeworkhelp.html