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2.1 Conditional StatementsPowerPoint Presentation

2.1 Conditional Statements

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Standards/Objectives:

- Students will learn and apply geometric concepts.
- Objectives:
- Recognize and analyze a conditional statement
- Write postulates about points, lines, and planes using conditional statements.

Assignment:

- Pp. 75-77 #4-28 all, 46-49 all.

Conditional Statement

- A logical statement with 2 parts
- 2 parts are called the hypothesis & conclusion
- Can be written in “if-then” form; such as, “If…, then…”

Conditional Statement

- Hypothesis is the part after the word “If”
- Conclusion is the part after the word “then”

Ex: Underline the hypothesis & circle the conclusion.

- If you are a brunette, then you have brown hair.
hypothesis conclusion

Ex: Rewrite the statement in “if-then” form

- Vertical angles are congruent.
If there are 2 vertical angles, then they are congruent.

If 2 angles are vertical, then they are congruent.

Ex: Rewrite the statement in “if-then” form

- An object weighs one ton if it weighs 2000 lbs.
If an object weighs 2000 lbs, then it weighs one ton.

Counterexample

- Used to show a conditional statement is false.
- It must keep the hypothesis true, but the conclusion false!
- It must keep the hypothesis true, but the conclusion false!
- It must keep the hypothesis true, but the conclusion false!

Ex: Find a counterexample to prove the statement is false.

- If x2=81, then x must equal 9.
counterexample: x could be -9

because (-9)2=81, but x≠9.

Negation

- Writing the opposite of a statement.
- Ex: negate x=3
x≠3

- Ex: negate t>5
t 5

Converse

- Switch the hypothesis & conclusion parts of a conditional statement.
- Ex: Write the converse of “If you are a brunette, then you have brown hair.”
If you have brown hair, then you are a brunette.

Inverse

- Negate the hypothesis & conclusion of a conditional statement.
- Ex: Write the inverse of “If you are a brunette, then you have brown hair.”
If you are not a brunette, then you do not have brown hair.

Contrapositive

- Negate, then switch the hypothesis & conclusion of a conditional statement.
- Ex: Write the contrapositive of “If you are a brunette, then you have brown hair.”
If you do not have brown hair, then you are not a brunette.

The original conditional statement & its contrapositive will always have the same meaning.

The converse & inverse of a conditional statement will always have the same meaning.

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