Deductive Structure Lesson 1.7. Deductive Structure: Conclusions are justified by means of previously assumed or provided statements.

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Presentation transcript:

Deductive Structure Lesson 1.7

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 of a definition & it’s converse: 1If a point is the midpoint of a segment, then the point divides the segment into 2 congruent segments. 2If a point divides a segment into 2 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.”

Converse: Of p implies q is q implies p p qq p Theorem: math statement you can prove Come with number Can’t use Theorem 1 to prove Theorem 1.

Theorems and postulates are not always reversible! If 2 <‘s are right <‘s, then they are congruent. Converse: If 2 <‘s are congruent, then they are right <‘s. True False

T or F? Conditional statement and converse. If an animal is a dog, then it has four legs. If it has four legs, then the animal 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 T or F. If the students grade is between 80 and 90, then the student receives a B on the test. True