Proofs, Postulates, Theorems

What is the difference between a theorem and a postulate?

• A postulate is a statement that is assumed true without proof while a theorem is a true statement that can be proven.

• A theorem is a statement that is assumed true without proof while a postulate is a true statement that can be proven.

Why are Given Statement(s) Necessary?

• They show you read the question.

• They tell you what your end goal is.

• They list what you know and are necessary to complete a proof.

What does a proof always start with?

• Theorems

• Given Statement(s)

• Postulates

• Reasons

What property states that if

a = b and b = c then a = c?

• Equality Property

• Reflexive Property

• Transitive Property

• Associative Property

Fill in the blanks to complete the geometric proof:

• ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

How can you prove step #2?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

How can you prove step #5?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

How can you prove step #4?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

Identify the  missing statement or reason

• Given

• Vertical Angles Theorem

• Definition of Angle Bisector

• Alternate Interior Angles Theorem