Bi-Conditionals and Definitions Accurately interpret and use words and phrases in geometric proofs such as "if…then," "if and only if," "all," and "not." Recognize the logical relationships between an "if…then" statement and its inverse, converse and contrapositive.

Guiding Question: How do conditional statements define terms? Lesson Obj: Iwbat determine if conditional statements define a term and write a bi-conditional for the term. For the following statement “Even numbers can be divided by 2” 1. Write the conditional 2. Write the converse 3. Write the inverse 4. Write the contrapositive

Guiding Question: How do conditional statements define terms? Consider the conditional and converse of your statements. Are they true? “If a number is even, then it can be divided by 2” (Conditional) “If a number can be divided by 2, then it is even” (Converse) Since they are both true, this is considered a definition!

Guiding Question: How do conditional statements define terms? Once you have a definition, you can re- write it as a bi-conditional statement (using if and only if). Ex. A number is even if and only if it can be divided by 2.

Guiding Question: How do conditional statements define terms? In Math this is how we determine definitions! Are both the converse and conditional statements true? What would the conditional and converse statements look like here? 2 parallel lines have a constant distance between them. What would the bi- conditional look like?

Guiding Question: How do conditional statements define terms? Can you come up with your own? Come up with 2 statements and test them. Assignment: Bi- conditional and definition WS