Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

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Presentation transcript:

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? StatementConclusionReason

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.

Give logical conclusions supported by reasons.  1 and  2 are right angles. Given m  1=90 o and m  2=90 o Definition of Right Angle m  1 = m  2 Transitive Property  1   2 Definition of Congruence RIGHT ANGLE CONJECTURE (RAC): All right angles are congruent.