2'1 Conditional Statements

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2.1 Conditional Statements

• Students will analyze and rewrite conditional and
  biconditional statements.
• Students will write the inverse, converse, and
  contrapositive of a conditional statement.

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What is a Conditional Statement?

• Conditional Statement
• a statement that has two parts, a hypothesis and
  a conclusion
• if-then form
• the if part contains the hypothesis and the
  then part contains the conclusion
• Example
• If it is noon in Maryland, then it is 9 a.m. in
  California.

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Rewrite in the following in if-then form

• Two points are collinear if they lie on the same
  line.
• 2.All sharks have a boneless skeleton.
• 3. A number divisible by 9 is also divisible by
  3.

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Write a Counterexample

• If x2 16, then x 4.
• If a number is odd, then it is divisible by 3.

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• Converse formed by switching the hypothesis and
  conclusion.
• Example
• Statement If you see lightning, then you hear
  thunder.
• Converse If you hear thunder, then you see
  lightning.

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Example

• Statement If two segments are congruent, then
  they have the same length.
• Converse

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• A statement can also be altered by a negation by
  writing the negative of the statement.
• Statement Negation
• m?A 300
  m?A ? 300
• ?A is acute.
  _________
  
• Inverse
• negating hypothesis and conclusion of a
  conditional statement
• Contrapositive
• negate the hypothesis and conclusion of the
  converse.

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• equivalent statements when two statements are
  both true or both false. A conditional statement
  is equivalent to its contrapositive.

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Now you try