Definitions and Biconditional Statements

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Presentation transcript:

Definitions and Biconditional Statements Geometry Chapter 2, Section 2

Notes Perpendicular Lines: lines that intersect 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”

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_________________________

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.