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Lesson 2-1

Conditional Statements. Lesson 2-1. Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Writing Conditional Statements. Hint: Turn the subject into the hypothesis. Example 1:. Vertical angles are congruent.

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Lesson 2-1

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  1. Conditional Statements Lesson 2-1 Lesson 2-1 Conditional Statements

  2. Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Writing Conditional Statements Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. Example 2: Seals swim. can be written as... Conditional Statement: If an animal is a seal, then it swims. Lesson 2-1 Conditional Statements

  3. Symbolic Logic • Symbols can be used to modify or connect statements. • Symbols for Hypothesis and Conclusion: Hypothesis is represented by “p”. Conclusion is represented by “q”. if p, then q or p implies q Continued….. Lesson 2-1 Conditional Statements

  4. Forms of Conditional Statements Converse: Switch the hypothesis and conclusion (q  p) pqIftwo angles are vertical, thenthey are congruent. qpIftwo angles are congruent, thenthey are vertical. Continued….. Lesson 2-1 Conditional Statements

  5. Forms of Conditional Statements Inverse:State the opposite of both the hypothesis and conclusion. (~p~q) pq :Iftwo angles are vertical, thenthey are congruent. ~p~q:Iftwo angles are not vertical, thenthey are not congruent. Lesson 2-1 Conditional Statements

  6. Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites. (~q~p) pq : Iftwo angles are vertical, thenthey are congruent. ~q~p:Iftwo angles are not congruent, thenthey are not vertical. Lesson 2-1 Conditional Statements

  7. Forms of Conditional Statements • Contrapositives are logically equivalent to the original conditional statement. • If pq is true, then qp is true. • If pq is false, then qp is false. Lesson 2-1 Conditional Statements

  8. Biconditional • When a conditional statement and its converse are both true, the two statements may be combined. • Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse:If an angle measures 90, then it is a right angle. Biconditional:An angle is right if and only if it measures 90. Lesson 2-1 Conditional Statements

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