2'2 Definitions

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2.2 Definitions Biconditional Statements

• p.79

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Perpendicular Lines

• 2 lines that intersect to form a right angle.

l
l m
m
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Line perpendicular to a plane

• A line that intersects a plane in a point is
  perpendicular to every line in the plane that
  intersects the line.

l
Q
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• Definitions can be written in if-then form.
• The converse of a definition is always true.
• This means the defn. is true forwards
  backwards.

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Ex True or False? Why?

• a.) D, B, E are collinear.
• True
• Def. of collinear
• b.) AC DB
• True
• Def. of lines
• c.) ltAEB is adjacent to ltCED
• False
• dont share a common side

A C
D E B
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only-if form

• Easy to spot, because it has the words only if
  in the middle of the statement.
• Ex It is Saturday, only if I am working at the
  mall.
• hypothesis? conclusion?
• Can rewrite in if-then form.
• Ex If I am working at the mall, then it is
  Saturday.

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Biconditional Statement

• Contains the phrase if only if
• Abbr. iff
• It is a conditional statement its converse all
  in one.
• Ex 3 points are collinear iff they are on the
  same line.
• Conditional If 3 pts are collinear, then they
  are on the same line.
• Converse If 3 pts are on the same line, then
  they are collinear.

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A biconditional is true only if the original
conditional AND its converse are true!
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Ex Is the statement a biconditional? Is the
statement true?

• x3 if only if x29.
• Yes, its a biconditional.
• Orig. Conditional statement?
• If x3, then x29.
• Converse?
• If x29, then x3.
• True or False?
• Biconditional is False

True
False
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A conditional statement its converse can be
rewritten as a biconditional only if both
statements are true.
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Ex Determine whether the statements are true.
If so, rewrite as one biconditional statement.

• Conditional If a ends in 0 or 5, then it is
  evenly divisible by 5.
• Converse If a is evenly divisible by 5, then
  it ends in 0 or 5.
• True or False?
• Biconditional?
• A ends in 0 or 5 iff it is divisible by 5.

True
True
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Assignment