2.2 Biconditionals and Definitions

2.2 Biconditionals and Definitions Chapter 2: Reasoning and Proof

2.2 Biconditionals and Definitions When a conditional and its converse are true, you can combine them into a true biconditional. Use the phrase “if and only if.”

Writing a Biconditional Conditional: If two angles have the same measure, then the angles are congruent. Converse: Biconditional:

Writing a Biconditional Conditional: If three points are collinear, then they lie on the same line. Converse: Biconditional:

Separating a Biconditional Biconditional: “A number is divisible by 3 if and only if the sum of its digits is divisible by 3.” Statement 1: Statement 2: * Look in book at summary on page 76

Definitions A good definition: • Uses clearly understood terms • Is precise. Avoid words such as large, sort of, and some. • Is reversible. You can write a good definition as a biconditional.

Writing a Definition as a Biconditional Definition: “Perpendicular lines are two lines that intersect to form right angles.” Conditional: “If two lines are perpendicular, then they intersect to form right angles.” Converse: “If two lines intersect to form right angles, then they are perpendicular.” Biconditional: “Two lines are perpendicular if and only if they intersect to form right angles.”

Writing a Definition Definition: “A right angle is an angle whose measure is 90.” Conditional: Converse: Biconditional:

Is the statement a good definition? a. An airplane is a vehicle that flies. b. A triangle has sharp corners. c. A square is a figure with four right angles.

Homework Pg 78 2 – 30even, 50 – 54all

2.2 Biconditionals and Definitions