Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions.

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Presentation transcript:

Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions

Biconditionals when a conditional and its converse are true, you can combine them as a true biconditional connects the conditional and its converse with the word “and” written shorter by using “if and only if”

Example 1 Write the converse. If the converse is also true, combine the statements as a biconditional: If two angles have the same measure, then the angles are congruent.

Quick Check 1 Write the converse. If the converse is also true, combine the statements as a biconditional: If three points are collinear, then they lie on the same line.

Example 2 Write two statements that form the biconditional: A number is divisible by 3 if and only if the sum of its digits is divisible by 3.

Quick Check 2 Write two statements that form this biconditional: A number is prime if and only if it has only two distinct factors, 1 and itself.

Summary biconditional statements: p↔q p if and only if q

Definitions A good definition: statement that help you identify or classify an object uses clearly understood terms precise reversible

Example 3 Show that this definition of perpendicular lines is reversible. Then, write it as a true biconditional: Perpendicular lines are two lines that intersect to form right angles.

Quick Check 3 Show that the definition of right angle is reversible. Then, write it as a true biconditional: A right angle is an angle whose measure is 90.