Transcript 2.2_Definitions_and_Biconditional_Statements_Notes_(GEO)

Definitions and
Biconditional Statements
Geometry
Chapter 2, Section 2
Notes
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Perpendicular Lines: lines that intersect
to form a right angle
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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.
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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.
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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.
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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.
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For a biconditional statement to be true, both the
conditional statement and its converse must be
true.