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Introduction to Geometric Proof
Logical Reasoning and Conditional Statements
Geometry involves deductive reasoning.
It uses facts, definitions, accepted properties, and laws of logic to form a logical argument.
Writing a geometric proof is a good way to practice logical reasoning!
A proof is a logical argument that shows a statement is true. It can be in the form of a two-column proof, a flowchart proof, a paragraph proof, an algebraic proof, or even proof without words.
Logical Reasoning
• Making logical statements or conclusions based on given conditions
• Statements are justified by definitions, postulates, theorems or “conjectures”
• Example:If __________________ , then ___________________ .
Why is this always true?
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
Try this!
• Given:
• Conclusion:
How about this?
Statement Conclusion Reason
How about this?
How about this?
Geometric Proof
- a sequence of statements from a GIVEN set of premises leading to a valid CONCLUSION
Each statement stems logically from previous statements.
Each statement is supported by a reason (definition, postulate, or “conjecture”).
EXAMPLE
Are vertical angles congruent?
2. Illustrate the given information.
1.Identify the GIVEN & what needs TO BE PROVEN.
EXAMPLE
3. Give logical conclusions supported by reasons.
TRY THIS!
Prove that All Right Angles are Congruent.
2. Illustrate the given information.
1.Identify the GIVEN & what needs TO BE PROVEN.
Two angles are right angles.
1
2
3. Give logical conclusions supported by reasons.
1 and 2 are right angles. Given
m1=90o and m2=90o
Definition of Right Angle
m1 = m2
Transitive Property
1 2
Definition of Congruence
RIGHT ANGLE CONJECTURE (RAC):
All right angles are congruent.