Conditional Statements youtube. com/watch SOL: G.1a SEC: 2.3.

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Presentation transcript:

Conditional Statements http://www. youtube. com/watch SOL: G.1a SEC: 2.3

Conditional Statement Definition: A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” “if p, then q”. Symbolic Notation p → q Lesson 2-1 Conditional Statements

Conditional Statement Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (Usually denoted p.) The hypothesis is the given information, or the condition. The conclusion is the part of an if-then statement that follows “then” (Usually denoted q.) The conclusion is the result of the given information. Lesson 2-1 Conditional Statements

Example Write the statement “ An angle of 40° is acute.” Hypothesis – An angle of 40° Represented by : p Conclusion – is Acute Represented by : q If – Then Statement – If an angle is 40°, then the angle is acute.

Example Identify the Hypothesis and Conclusion in the following statements: If a polynomial has six sides, then it is a hexagon. H: A polygon has 6 sides C: it is a hexagon Tamika will advance to the next level of play if she completes the maze in her computer game. H: Tamika Completes the maze in her computer game. C: She will advance to the next level of play. p q

Forms of Conditional Statements Conditional Statements: Formed By: Given Hypothesis and Conclusion. Symbols: p → q Examples: If two angles have the same measure then they are congruent.

Forms of Conditional Statements Converse: Formed By: Exchanging Hypothesis and conclusion of the conditional. Symbols: q → p Examples: If two angles are congruent then they have the same measure.

Forms of Conditional Statements Inverse: Formed By: Negating both the Hypothesis and conclusion of the conditional. Symbols: ~p →~q Examples: If two angles do not have the same measure they are not congruent.

Forms of Conditional Statements Contra - positive: Formed By: Negating both the Hypothesis and conclusion of the Converse statement. Symbols: ~q →~p Examples: If two angles are not congruent then they do not have the same measure.

Logically Equivalent Statements - are statements with the same truth values. Example: Write the converse, inverse and contra - positive of the following statement: Conditional: If a shape is a square, then it is a rectangle. Converse: If a shape is a rectangle, then it is a square. Inverse: If a shape is not a square, then it is not a rectangle. Contra-positive: If a shape is not a rectangle, then it is not a square.

Try This: Example: Write the converse, inverse and contra - positive of the following statement: Conditional: If two angles form a linear pair, then they are supplementary. Converse: Inverse: Contra – positive:

Assignments Classwork: WB: pg 39 - 40 all Homework: pg 93-95 6-24 even, 28, 32-34, 43-45