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Advanced Geometry Section 1.7 and 1.8- Deductive Structure / Statements of Logic. Learner Objective: Students will write the converse, inverse, and 
 contrapositive of a conditional statement, determine the truth 
 value of statements and will use the chain rule to make logical 
 conclusions.

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Advanced Geometry Section 1.7 and 1.8- Deductive Structure / Statements of Logic


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    1. Advanced Geometry Section 1.7 and 1.8- Deductive Structure / Statements of Logic Learner Objective: Students will write the converse, inverse, and 
 contrapositive of a conditional statement, determine the truth 
 value of statements and will use the chain rule to make logical 
 conclusions.

    2. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. 1 A B C D E

    3. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Building blocks of Geometry: Undefined Terms - Terms which we can't officially 
 define. We describe their properties but don't 
 formally define them.  examples: point, line, plane Definitions - State the meaning of a term. There is 
 never a need to prove a definition. (It is true 
 because we say it is true.)  examples: Def. of a right angle, Def. of a  
 segment bisector...

    4. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Building blocks of Geometry (cont.): Postulates - An unproved assumption. These are pretty 
 obvious statements which we are unable to prove but 
 which clearly must be true.  example: Two points determine a line. Theorems - A mathematical statement which can be 
 proved.  example: If two angles are both right angles, 
 then they are congruent.

    5. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Definitions, Postulates and Theorems are all conditional 
 statements. They have some (sufficient) condition that 
 leads to a (necessary) conclusion. If two angles are both right angles, Having two right angles is sufficient evidence to conclude 
that the angles are congruent. then they are congruent. When two angles are both right angles, it is necessary to 
conclude that they are congruent (they have to be). What happens if we reverse the condition and conclusion?

    6. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Here is the theorem with the condition and conclusion reversed: If two angles are congruent Is knowing that two angles are congruent sufficient 
evidence to conclude that they must be right angles? then they are both right angles. If two angles are congruent, is it necessary to conclude 
that they are right angles? Is this a true statement? For a statement to be considered true, it must ALWAYS be 
 true. NOT ALWAYS TRUE = FALSE

    7. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Conditional statements can be written in "If p then q" form 
where p is the condition or hypothesis of the statement 
(trigger) and q is the conclusion (result). "If p then q" can be symbolized (also read "p implies q")

    8. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Reversing the condition and the conclusion results in the 
Converse of the original statement. Thus the convers is 
symbolized If both the conditional and the converse are true, the 
statement is said to be reversible. Definitions are always reversible. Postulates and Theorems are sometimes reversible.

    9. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. The Negation (opposite) of the statement p is "not p" and 
is symbolized The Inverse of the conditional statement is formed when 
we negate both p and q. Thus the inverse is symbolized

    10. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. The Contrapositive of the conditional statement is formed 
by both reversing and negating p and q. Thus, the 
contrapositive can be symbolized

    11. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. The conditional statement and it's contrapositive have the 
same "truth value". That is, they are either both true or 
both false. The inverse and the converse have the same truth value.

    12. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Example Conditional: If two angles are both right angles, 
then they are congruent Converse: If two angles _______________ then ______________________ Inverse: If two angles _______________ then ______________________ Contrapositive: If two angles _______________ then ______________________

    13. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Example If an angle is an acute angle, then its measure is greater than 0 and less than 90. Conditional: Converse: If an angle _____________________________, then __________________________________. Inverse: If an angle _____________________________, then __________________________________. Contrapositive: If an angle _____________________________, then __________________________________.

    14. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. A series of conditional statements can be connected 
together using the Chain Rule. If and then

    15. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. Example: , , and ,

    16. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. At Hilldale High School, there is a rule that any student caught fighting 
must be given a three day suspension. Bill, Bob and Bo are all students 
at Hilldale. Which of the following statements is/are true? Bill has been given a three day suspension so we know that he 
 must have been caught fighting. Bob has never been caught fighting, so we know that he has 
 never been given a three day suspension. Bo has never been given a three day suspension, so we know 
 that he has never been caught fighting.

    17. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. At Hilldale High School, there is a rule that any student caught fighting 
must be given a three day suspension. Bill, Bob and Bo are all students 
at Hilldale. Which of the following statements is/are true? Conditional: If fighting then suspension. Bill has been given a three day suspension so we know that he 
 must have been caught fighting. Converse: If suspension then fighting False It is not necessary for someone to Fight in order to receive a 
suspension. Bill could have been suspended for something else. 
The converse is false.

    18. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. At Hilldale High School, there is a rule that any student caught fighting 
must be given a three day suspension. Bill, Bob and Bo are all students 
at Hilldale. Which of the following statements is/are true? Conditional: If fighting then suspension. Bob has never been caught fighting, so we know that he has 
 never been given a three day suspension. Inverse: If NOT fighting then NO suspension. False Fighting is a sufficient condition to receive a suspension but not 
a necessary one. Bob could have been suspended for something 
else. The inverse is false.

    19. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions. At Hilldale High School, there is a rule that any student caught fighting 
must be given a three day suspension. Bill, Bob and Bo are all students 
at Hilldale. Which of the following statements is/are true? Conditional: If fighting then suspension. Bo has never been given a three day suspension, so we know 
 that he has never been caught fighting. If NO suspension then NOT fighting. Contrapositive: True Since suspension is a necessary result of fighting, NOT being 
suspended is sufficient to conclude that there was NO fighting. 
The contrapositive is true.

    20. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    21. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    22. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    23. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    24. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    25. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    26. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    27. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    28. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    29. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    30. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    31. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    32. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    33. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    34. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    35. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    36. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.

    37. Learner Objective: Students will write the converse, inverse, and contrapositive of a 
 conditional statement, determine the truth value of statements and will use the 
 chain rule to make logical conclusions.