2.2 Conditional Statements

GeometryChapter 2: Reasoning and Proof

Conditional Statements

• Conditional Statement is an if-then statement.– Written p → q, read “if p then q” or “p implies q”– Ex: If today is Friday, Then tomorrow is Saturday.

• Hypothesis is the part p following if.– Today is Friday

• Conclusion is the part q following then.– Tomorrow is Saturday

I.D. Please

If an animal is a robin, then the animal is a bird.

Hypothesis (p): An animal is a robin.

Conclusion (q): The animal is a bird

Make me Conditional

• Vertical angles share a vertex

1. Identify hypothesis and conclusion.Vertical angles share a vertex.

2. Write it as a conditional statement.If two angles are vertical, then they share a vertex.

Try it!

• Dolphins are mammals.

Tell Me the Truth

• Truth Value – is the statement true or false.

• Is the conditional true or false? If false, find counterexample.– If a woman is Hungarian, then she is European.• True

– If a number is divisible by 3, then it is odd.• False, example: 12

Birthday Birthday!If it is your birthday, then you will have cake.

1. It is your birthday, you have cake.True True True

2. It is your birthday, you do not have cake.True False False

3. It is not your birthday, you have cake.False True True

4. It is not your birthday, you do not have cake.False False True

True or False?

• If a month has 28 days, then it is February.

• If two angles form a linear pair, then they are supplementary.

NEGATIVE!!!

• Negation – the opposite of a statement.– Ex: opposite o statement p is ~p and read not p

– P: The sky is blue– ~P: The sky is not blue.

Shoe Time

Converse – Switch the hypothesis and conclusion of a conditional statement– Written q → p, read “if q then p”– If tomorrow is Saturday, then today is Friday.

Conditional: If a figure is a rectangle, then it has four sides.

CONVERSE:

Negative Nancy

Inverse – Negate both the hypothesis and the conclusion of the conditional– Written ~ p → ~q, read “if not p then not q”– If today is not Friday, then tomorrow is not Saturday.

Conditional: If a figure is a rectangle, then it has four sides.

INVERSE: If a figure is not a rectangle, then it does not have four sides.

Make the Opposite

Contrapositive – Negate both the hypothesis and the conclusion of the converse– Combine the converse and the inverse– Written ~ q → ~p, read “if not q then not p”– If tomorrow is not Saturday, then today is not Friday.

Conditional: If a figure is a rectangle, then it has four sides.

CONTRAPOSITIVE: If a figure does not have four sides, then it is not a rectangle.

Family Affair

• Think of Conditional Statements as a Family– Conditional statements – normal child– Converse – Same but different– Inverse - Pessimistic– Contrapositive – COMPLETE opposite

Equivalent Statements

• Statements with the same truth value.

Practice TimeWorksheet #1-14

Hypothesis and ConclusionConditional Statements

True or False – counterexamplesConverse, Inverse, Contrapositive

Symbolic Notation