Geometry unit 2.3
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The document defines and provides examples of conditional statements, converses, and biconditionals ("if and only if" or "iff" statements). It explains that a biconditional combines a conditional statement with its converse, making the statement true in both directions. Examples show biconditionals used to define mathematical and geometric relationships, such as a number being divisible by 5 iff it ends in 0 or 5. Definitions are also explained to be reversible, and can thus be written as biconditionals.
Geometry unit 2.3
- 2. Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in one. Ex: 3 points are collinear iff they are on the same line. Conditional: If 3 pts are collinear, then they are on the same line. Converse: If 3 pts are on the same line, then they are collinear.
- 4. x=3 if and only if x2=9. Yes, it’s a biconditional. Orig. Conditional statement? If x=3, then x2=9. Converse? If x2=9, then x=3. True or False? Biconditional is False True False, x could be -3
- 6. Conditional: If a # ends in 0 or 5, then it is evenly divisible by 5. TTrruuee Converse: If a # is evenly divisible by 5, then it ends in 0 or 5. True or False? TTrruuee Biconditional? A # ends in 0 or 5 iff it is divisible by 5.
- 7. •Definitions can be written in “if-then” form. •The converse of a definition is always true. •This means the defn. is true forwards & backwards. BICONDITIONAL!!!
- 8. Show that the definition of right angle is reversible. Then write it as a biconditional. •Definition: A right angle is an angle whose measure is 90.
- 9. CCoonnddiittiioonnaall:: An angle is a right angle then the angle measures 90 degrees CCoonnvveerrssee:: True An angle is 90 degrees then it is a right angle BBiiccoonnddiittiioonnaall An angle is a right angle iff it measures 90 degrees
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