Lesson 2-3

Conditional Statements

Lesson 2-3

Lesson Outline

Five-Minute Check

Then & Now and Objectives

Vocabulary

Key Concept

Examples

Lesson Checkpoints

Summary and Homework

Lesson 2-3

Then and Now

You used logic and Venn diagrams to determine truth values of negations, conjunctions, and disjunctions. (Lesson 2–2)

• Analyze statements in if-then form.

• Write the converse, inverse, and contrapositive of if-then statements.

Lesson 2-3

Objectives

• Analyze statements in if-then form

• Write the converse, inverse and contrapositive of if-then statements

Lesson 2-3

Vocabulary• Implies symbol (→)• Conditional statement – a statement written in if-then

form • Hypothesis – phrase immediately following the word

“if” in a conditional statement • Conclusion – phrase immediately following the word

“then” in a conditional statement • Converse – exchanges the hypothesis and conclusion

of the conditional statement • Inverse – negates both the hypothesis and conclusion

of the conditional statement • Contrapositive – negates both the hypothesis and

conclusion of the converse statement • Logically equivalent – multiple statements with the

same truth values • Biconditional – conjunction of the conditional and its

converse

Lesson 2-3

Key Concept

Lesson 2-3

Example 1A

A. Identify the hypothesis and conclusion of the following statement.

Answer: Hypothesis: A polygon has 6 sides.Conclusion: It is a hexagon.

If a polygon has 6 sides, then it is a hexagon.

If a polygon has 6 sides, then it is a hexagon.

hypothesis conclusion

Lesson 2-3

Example 1B

B. Identify the hypothesis and conclusion of the following statement.

Tamika will advance to the next level of play if she completes the maze in her computer game.

Answer: Hypothesis: Tamika completes the maze in her computer game.Conclusion: She will advance to the next level of play.

Lesson 2-3

Example 2A

A. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form.

Measured distance is positive.

Answer: Hypothesis: A distance is measured.Conclusion: It is positive.

If a distance is measured, then it is positive.

Lesson 2-3

Example 2B

B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form.

A five-sided polygon is a pentagon.

Answer: Hypothesis: A polygon has five sides.Conclusion: It is a pentagon.

If a polygon has five sides, then it is a pentagon.

Lesson 2-3

Example 3A

A. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

If you subtract a whole number from another whole number, the result is also a whole number.

Answer: Since you can find a counterexample, the conditional statement is false.

Counterexample: 2 – 7 = –5

2 and 7 are whole numbers, but –5 is an integer, not a whole number.

The conclusion is false.

Lesson 2-3

Example 3B

B. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

If last month was February, then this month is March.

Answer: So, the conditional statement is true.

When the hypothesis is true, the conclusion is also true, since March is the month that follows February.

Lesson 2-3

Example 3C

C. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

When a rectangle has an obtuse angle, it is a parallelogram.

Answer: So, the conditional statement is true.

The hypothesis is false, since a rectangle can never have an obtuse angle. A conditional with a false hypothesis is always true.

Lesson 2-3

Key Concept

Lesson 2-3

Key Concept

Lesson 2-3

Example 4A

NATURE Write the converse, inverse, and contrapositive of the following true statement. Determine the truth value of each statement. If a statement is false, give a counterexample.

Bats are animals that can fly.

Bats are not birds, they are mammals. Bats have modified hands and arms that serve as wings.

They are the only mammals that can fly.

Conditional: First, rewrite the conditional in if-then form.

If an animal is a bat, then it can fly.

This statement is true.

Lesson 2-3

Example 4 cont

Converse: If an animal can fly, then it is a bat.

Counterexample: A bird is an animal that can fly, but it is not a bat.

The converse is false.

Inverse: If an animal is not a bat, then it cannot fly.

Counterexample: A bird is not a bat, but it is an animal that can fly.

The inverse is false.

Contrapositive: If an animal cannot fly, then it is not a bat.

The converse is true.

Lesson 2-3

Lesson Checkpoints

Conditional If two lines are perpendicular, then their angle is right.

Converse

Inverse

Contrapositive

Conditional

Converse If two angles are supplementary, then they sum to 180º

Inverse

Contrapositive

Conditional

Converse

Inverse If today is not Friday, then we do not have a quiz.

Contrapositive

Conditional

Converse

Inverse

Contrapositive If two angles aren’t a linear pair, then they aren’t supplementary.

Lesson 2-3

Conditionals in Symbols

Statements Symbology

Conditional P →Q

Converse Q→P

Inverse ~P →~Q

Contrapositive ~Q→~P

Lesson 2-3

Summary & Homework

• Summary:– A polygon is a closed figure made of line segments– The perimeter of a polygon is the sum of the lengths

of its sides– The perimeter of a circle is called the circumference– The area of a two-dimensional figure can be

determined by formulas on the formula sheet

• Homework: – pg 70-3: 18-23