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Definitions and Biconditional Statements
Geometry Chapter 2, Section 2
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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”
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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_________________________
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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.
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