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:

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• Given:

• Conclusion:

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• Given:

• Conclusion:

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• Given:

• Conclusion:

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• 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.