1.  Aim: How do we think like a mathematician? Do Now: July 16, 2012 1. Name all the geometric relationships found in the image below. (i.e. EB ≅ CH) 2. What other relationship information could you infer from the given information?

2. Things to look out for: Vocabulary Words  Negation  Inverse (Logic)  Converse (Logic)  Contrapositive  Bi-conditional Khan Academy Week 2  Segment Addition Segment Addition  Midpoint of a Segment Midpoint of a Segment  Conditional Statements Conditional Statements  Converse, Inverse, and Contrapositive Converse, Inverse, and Contrapositive  Logical Arguments and Deductive Reasoning Logical Arguments and Deductive Reasoning  Conditional Statements and Truth Value Conditional Statements and Truth Value

3. Agenda  Read “Interpreting Diagrams.PDF” and complete the “Review Questions” found at http://www.ptechnyc.org/page/114http://www.ptechnyc.org/page/114  Complete the assignment you started yesterday found here: Transversals and Triangle Sum Proof.doc Transversals and Triangle Sum Proof.doc  Read through the 4 lessons found at: http://www.regentsprep.org/regents/math/geometry/GP2/index GP2.htm http://www.regentsprep.org/regents/math/geometry/GP2/index GP2.htm  Complete the writing exercise found in the next two slides.  If you finish before class ends. Work on the Khan Academy assignments listed in the previous slide. Assignments should be done in order. All completed assignments should be left in your class folder.

4. Alice in Wonderland "Then you should say what you mean." the March Hare went on. "I do," Alice hastily replied; "at least -- at least I mean what I say -- that's the same thing, you know." "Not the same thing a bit!" said the Hatter, "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!" "You might just as well say," added the March Hare, "that 'I like what I get' is the same thing as 'I get what I like'!" "You might just as well say," added the Dormouse, who seemed to be talking in his sleep, "that 'I breathe when I sleep' is the same thing as 'I sleep when I breathe'!" "It is the same thing with you," said the Hatter, and here the conversation dropped, and the party sat silent for a minute. Read through the following passage and answer the questions on the next page. Lewis Carroll, the author of Alice's Adventures in Wonderland and Through the Looking Glass, was actually a mathematics teacher. As a hobby, Carroll wrote stories that contain amusing examples of logic.

5. Writing Exercise  When the Dormouse says "that 'I breathe when I sleep' is the same thing as 'I sleep when I breathe'!”, these statements could be rewritten as the following conditional statements.  If I am sleeping, then I am breathing. If I am breathing, then I am sleeping.  Write 2 paragraphs (or more) explaining why switching the statements does not always work. Be sure to answer the following questions in your paragraph.  Which related conditional is this?(Converse, Inverse, Contrapositive)  What would the statement look like in the other forms? Would they be true or false?  Define the term “Bi-conditional statement” and explain the difference from a conditional statement. Give examples.