Unit 3: Polygons in the Plane

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Unit 3 Polygons in the Plane

• Conditional Statements Vocabulary

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What is a statement?

• A statement is a sentence that is either true or
  false, but not both.
• Example The Atlanta Thrashers are a pro
  basketball team.
• Non example Whats your favorite music video?

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What is a conjecture?

• A conjecture is an unproven statement that is
  based on observations.

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What is a conditional statement?

• A conditional statement has the form if p, then
  q which can be written as p gt q.
• p is called the hypothesis and q is called the
  conclusion.

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What is the inverse of a statement?

• The inverse (or negation) of a conditional
  statement is the opposite of the original
  statement. p gt q

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What is the converse of a statement?

• The converse of a conditional statement is formed
  by interchanging the hypothesis and the
  conclusion.
• For instance, the converse of p gt q is q gt p.

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• A conditional statement may be true or false, and
  its converse may be true or false.
• To prove that a conditional statement is true,
  you must present an argument that the conclusion
  follows for all cases that fulfill the hypothesis.

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What is a counterexample of a statement?

• A counterexample is a an example of a conditional
  statement in which the hypothesis is fulfilled
  and the conclusion is not fulfilled proves that
  the statement is false.

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What is the contrapositive of a statement?

• The contrapositive of a conditional statement p
  gt q is the inverse of the converse. q gt
  p
• The contrapositive of a conditional statement is
  true if and only if the conditional statement is
  true.

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What is a biconditional statement?

• The biconditional statement , p if and only if
  q is written as p ? q.
• This single statement is equivalent to writing
  the conditional statement p gt q and its
  converse q gt p.
• When a statement and its converse are both true,
  you can write them as a single biconditional
  statement.

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• Complete the graphic organizer for the following
  statement.
• An angle is obtuse when it measures more than
  90.