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### Conditional Statementshttp://www.youtube.com/watch?v=Wnc3_AekOno&feature=relatedhttp://www.youtube.com/watch?v=vzuaHRJAHuQ

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 conclusionis 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:

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