Section 2.1 Conditional Statements

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Presentation transcript:

Section 2.1 Conditional Statements A CONDITIONAL statement, a type of logical statement, has 2 parts, a Hypothesis and a Conclusion. When the statement is written in the if-then form, the "if" part contains the hypothesis and the "then" part contains the conclusion.

COUNTER EXAMPLES are used to prove a conditional statement's conclusion to be false.

Converse Statements

Negations - the negative of a statement. Inverse - when you negate the hypothesis and conclusion of a conditional statement. Contrapositive - when you negate the hypothesis and conclusion of the converse of a conditional statement. A conditional statement and its contrapositive are equivalent. An inverse and a converse are equivalent.

Section 2.2 Definitions and Biconditional Statements A biconditional statement is a statement that contains the phrase, "if and only if." Writing a biconditional statement is equivalent to writing a conditional statement and its converse when both statements are true. When the converse is false, a true biconditional statement cannot be written.

Writing a biconditional statement.

For each conditional, write the converse and biconditional. 1. If the date is July 4th, then it is Independence day. 2. If points lie on the same line, then they are collinear.

An example of where a true biconditional statement cannot be written.

Section 2.3 Deductive reasoning Using Symbolic Notation:

1. If the car will start, then the battery is charged. 2. If the battery is charged, then the car will start. 3. If the car will not start, then the battery is not charged. 4. If the battery is not charged, then the car will not start. The conditional and its contrapositive are TRUE. The converse and inverse are FALSE.

2 Laws of Deductive Reasoning

Section 2.4 Reasoning with Properties from Algebra

Ex. 1 Solve 5x - 18 = 3x + 2 and write a reason for each step. 5x - 18 = 3x + 2 Given 2x - 18 = 2 Subtraction prop. of equality 2x = 20 Add. prop. of equality x = 10 Division prop. of equality Ex. 2 Solve 55x -3(9x + 12) = -64 and write a reason for each step.

Section 2.5 Proving Statements about Segments

Ex. 1

Ex 2. Two-Column Proof Given: LK = 5, JK = 5, JK JL Prove: LK JL Statements Reasons 1. 1. Given 2. 2. Given 3. LK = JK 3. Transitive prop. 4. LK JK 4. 5. JK JL 5. Given 6. 6. Trans. prop.

Section 2.6 Proving Statements about Angles Relexive Symmetric Transitive

Congruent Supplements Theorem Congruent Complements Theorem