2.2 Definitions and Biconditional Statements

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Presentation transcript:

2.2 Definitions and Biconditional Statements Recall: A definition uses known words to describe a new word. Perpendicular Lines ( ): Two lines that intersect to form a right angle. A line perpendicular to a plane: A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it. T m n T n m { n P T n P

Biconditional Statements Biconditional: When a conditional and its converse are both true they can be combined into one statement using “if and only if” (iff). Writing a biconditional statement is equivalent to writing a conditional and its converse. If an angle is a right angle, then its measure is 90. Converse: If the measure of an angle is 90, then it is a right angle. Are both of these statements true? An angle is a right angle if and only if its measure is 90.

Rewriting a Biconditional Statement Biconditionals can be rewritten as a conditional and its converse. Three lines are coplanar if and only if they lie in the same plane. Conditional: If three lines are coplanar, then they lie in the same plane. Converse: If three lines lie in the same plane, then they are coplanar. Analyze the following statement. x = 3 if and only if x2 = 9. Is this a biconditional statement? Is the statement true?

Knowing how to use true biconditional statements is an important tool for geometry. If you can write a biconditional statement that is true then you can use the conditional statement or its converse to justify an argument. Can the Segment Addition Postulate be written as a biconditional statement? If B lies between A and C, then AB + BC = AC. Converse: Point B lies between points A and C if and only if AB + BC = AC.