1.What is the difference between a paragraph proof and a column proof? 2.True or False: If a quadrilateral is a square, then all four sides are congruent.

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Presentation transcript:

1.What is the difference between a paragraph proof and a column proof? 2.True or False: If a quadrilateral is a square, then all four sides are congruent. If all four sides of a quadrilateral are congruent, then the figure is a square.

1.7 Deductive Structure Deductive structure: conclusions are justified by means of previously assumed or provided statements.

Four Elements: 1.Undefined terms 2.Assumptions known as postulates 3.Definitions 4.Theorems and other conclusions

Postulate: an unproven assumption Definition: states the meaning of a term, they are ALWAYS reversible!

Example stated: 1If a point is the midpoint of a segment, then the point divides the segment into two congruent segments. 2If a point divides a segment into two congruent segments, then the point is midpoint of the segment.

Conditional Statement: phypothesis: “If ” part of the statement. qconclusion: “Then” part of the statement. LOGIC: p q (read) “If p, then q.” “p implies q.”

Theorem: Math statement you can prove Can’t use a theorem to prove itself Converse: If p implies q, does q imply p? p qq p

Theorems and postulates are not always reversible! If two angles are right angles, then they are congruent. True Is the converse also true? If two angles are congruent, then they are right angle. NO!

True or False? Conditional statement and converse. If an animal is a dog, then it has four legs. If an animal has four legs, then it is a dog. False!

If a student receives a B on the test, then his/her grade is between 80 and 90. State the converse and tell if it is true or false. If the students grade is between 80 and 90, then the student receives a B on the test. True.