Definitions and Biconditional Statements

1. Definitions and Biconditional Statements Geometry Chapter 2, Section 2

2. Notes • Perpendicular Lines: lines thatintersect to form a right angle • Example: ceiling tiles • A line perpendicular to a plane intersects the plane at a single point and is perpendicular to every line in the plane that it intersects. • ┴ this symbol is read “ is perpendicular to”

3. Special Property of definitions: all definitions can be interpreted forward and backwards, i.e. the statement of the definition and its converse are both true. • If two lines are ┴ each other, then they intersect to form a right angle, and • If two lines intersect to form a right angle, then the two lines are ┴. • On Your Own: Write the converse of the definition of congruent segments. • If segments are congruent, then they have the same length. • Converse: ____________________________ • Is the statement and its converse true? Explain why or why not_________________________

4. When the original statement and its converse are both true, we can show this by using the phrase “if and only if” which can be abbreviated iff. • Two lines are ┴ to each other iff they intersect to form right angles. • This type of statement is called a biconditional statement. • On Your Own: Write the biconditional of the definition of congruent segments. • ______________________________________ • For a biconditional statement to be true, both the conditional statement and its converse must be true.