Biconditionals and Definitions

Warm-up Write the converse, inverse and contrapositive of the following conditional. If Boulder gets 15 inches of rain, then we don’t have school. Converse: Inverse: Contrapositive:

Objectives: 1) To write biconditionals 2) To recognize good definitions

Biconditional Biconditional: When a conditional and its converse are true, you can join the two parts with the phrase if and only if

Example If you are in Washington D.C, then you are in the United States Capital. Converse If you are in the United States Capital, then you are in Washington D.C. Biconditional You are in Washington D.C. if and only if you are in the United States Capital. or You are in the United States Capital if and only if you are in Washington D.C.

Example 2 If two angles have the same measure, then the angles are congruent Converse Biconditional

Example 3 If three points are collinear, then they lie on the same line. Converse Biconditional

Identifying the Conditionals in a Biconditional Biconditional The number is positive if and only if it is above 0. Conditional Converse

A Good Definition……. 1) Uses clearly understood terms. 2 )Is precise. Good definitions avoid words such as large, sort of and almost. 3) Is reversible. That means you can write a good definition as a true biconditional.

Writing a Definition as a Biconditional Is this definition of quadrilateral reversible? If yes, write it as a true biconditional. Definition: A quadrilateral is a polygon with four sides Conditional: Converse: Biconditional:

Writing a Definition as a Biconditional Example 2 Is this definition of quadrilateral reversible? If yes, write it as a true biconditional. Definition: A straight angle is an angle that measures 180 Conditional: Converse: Biconditional:

2.3 Homework: Mathxlforschool.com Due midnight.