2.6 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 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
• Definitions
• Postulates
• Properties
• Theorems
Conclusion
2.6 Theorems
2.6 Theorems
2.6 Writing a Proof
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.
2.6 Tips
Helpful Hint
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.
2.6 Practice
Write the letter of the correct justification next
to each step. (Use one of them twice)
B
A
B
C
2.6 Proof
Statements
Reasons
1.
1. Given
2.
2.
3.
3. Substitution Prop. of =
4.
4.
2.6 Proof
Mark the diagram and answer the questions about the proof on the following
slide.
Statements
Reasons
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 Proofs
Copy 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_ch0
2_06_homeworkhelp.html