Mathematical Proofs

Geometric Proofs

Two Column Proofs

What is a Proof?

A Proof is a convincing mathematical argument.

Geometric Proof premises

• Definitions

• Postulates

• Properties

• previous proven theorems

Writing a Proof

• Justify each logical step with reason.

• You can use symbols and abbrev, but they must be clear and able to understand.

Multiple Choice

Give the reason that belongs in the blank labeled 1.

• Given

• Substitution Property of Equality

• 4x = 20

• Division Property of Equality

Multiple Choice

What is the reason for step #2?

• Definition of congruent segments

• Definition of congruent angles

• Definition of straight angle

• Definition of midpoint

Multiple Choice

What is the missing statement in the proof?

• Segment Addition Postulate

• Segment Multiplication property

• Segment Subtraction property

Multiple Choice

Name the property of equality or congruence that justifies going from the first statement to the second statement.

• Addition Property

• Multiplication Property

• Distributive Property
• Combine Like Terms

Multiple Choice

What is step 6

• Subtraction property of equality
• Addition property of equality
• Division property of equality

Multiple Choice

What is reason 3?

• Addition Property of Equality
• Subtraction Property of Equality
• Multiplication Property of Equality
• Division Property of Equality