Lesson 2-3: Conditional Statements TARGETS Analyze statements in if-then form. Write converses, inverses, and contrapositives. Targets

Content Standards G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. 6 Attend to precision. 8 Look for and express regularity in repeated reasoning. Targets

You used data to find patterns and make predictions. Analyze statements in if-then form. Write converses, inverses, and contrapositives. Targets

2-3 Vocabulary conditional statement if-then statement hypothesis conclusion related conditionals converse inverse contrapositive logically equivalent Targets

Revisit Compound Statements LESSON 2-3: Conditional Statements Let’s revisit Compound Statements. q A. p ^ q : p 4 7 15 B. p v q : C. ~ p ^ q : p: pizza for lunch q: fries for lunch D. p ^ ~ q : Revisit Compound Statements

LESSON 2-3: Conditional Statements Think about a situation that might be represented by this Venn Diagram. q p New Venn Diagram

Conditional Statement LESSON 2-3: Conditional Statements Conditional Statement A compound statement that can be written in the form of ‘If…, then…’ p  q , read as ‘if p, then q’ p: you are sick q: you have a make up assignment to complete If you are sick, then you have a make up assignment to complete OR If you are sick, you have a make up assignment to complete Conditional Statement

Hypothesis & Conclusion LESSON 2-3: Conditional Statements Conditional Statement has 2 parts: If you are sick, then you have a make up assignment to complete hypothesis conclusion Hypothesis & Conclusion

Conditional Statements LESSON 2-3: Conditional Statements If you are sick, then you have a make up assignment q p  q p Conditional Statements

Identify the hypothesis and conclusion of the following statements. LESSON 2-3: Conditional Statements EXAMPLE 1 Identify the Hypothesis and Conclusion Identify the hypothesis and conclusion of the following statements. A. If a polygon has 6 sides, then it is a hexagon. B. A number is divisible by 10 if its last digit is a 0. Example 1

Identify the hypothesis and conclusion of the following statements. LESSON 2-3: Conditional Statements EXAMPLE 1 Identify the Hypothesis and Conclusion Identify the hypothesis and conclusion of the following statements. C. If you are a baby, then you will cry. D. Another performance will be scheduled if the first one is sold out. Example 1

Conditional Statement LESSON 2-3: Conditional Statements Conditional Statement Can be written without using if and then To write statements in if-then form: 1. ID the Hypothesis 2. ID the Conclusion 3. Rewrite in ‘if…, then…’ form A mammal is a warm-blooded animal Conditional Statement

A. Measured distance is positive. LESSON 2-3: Conditional Statements EXAMPLE 2 Write a Conditional in If-Then Form Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. A. Measured distance is positive. B. A five-sided polygon is a pentagon. Example 2

C. Four quarters can be exchanged for a $1 bill. LESSON 2-3: Conditional Statements EXAMPLE 2 Write a Conditional in If-Then Form Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. C. Four quarters can be exchanged for a $1 bill. D. The sum of the measures of two supplementary angles is 180. Example 2

Truth Values of Conditional Statement LESSON 2-3: Conditional Statements Truth Values of Conditional Statement If Tom finishes his homework, then he will clean his room Truth Values of Conditional Statement

Truth Values of Conditional Statement LESSON 2-3: Conditional Statements Truth Values of Conditional Statement If Tom finishes his homework, then he will clean his room Hypothesis (p) Conclusion (q) Conditional (p  q) Tom finishes his homework Tom cleans his room If Tom finishes his homework, then he will clean is room A conditional is false ONLY when its hypothesis is true and conclusion is false When the hypothesis is false, the conditional will ALWAYS be true Truth Values of Conditional Statement

A. If you subtract a whole number from another whole LESSON 2-3: Conditional Statements EXAMPLE 3 Truth Values of Conditionals Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. A. If you subtract a whole number from another whole number, the result is also a whole number. B. If last month was February, then this month is March. Example 3

C. When a rectangle has an obtuse angle, it is a parallelogram. LESSON 2-3: Conditional Statements EXAMPLE 3 Truth Values of Conditionals Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. C. When a rectangle has an obtuse angle, it is a parallelogram. D. If yesterday was Tuesday, then today is Monday. Example 3

Lesson 2-3: Conditional Statements TARGETS Analyze statements in if-then form. Write converses, inverses, and contrapositives. Targets

Related Conditionals p  q LESSON 2-3: Conditional Statements Related Conditionals p  q If a polygon has 6 sides, then it is a hexagon. Converse: q  p , hypothesis & conclusion switch If a polygon is a hexagon, then it has 6 sides. Inverse: ~p  ~q , negate both hypothesis and conclusion If a polygon does not have 6 sides, then it is not hexagon. Contrapositive: ~q  ~p , negate both hypothesis and conclusion of the converse If a polygon is not a hexagon, then it does not have 6 sides. Related Conditionals

Related Conditionals p  q LESSON 2-3: Conditional Statements Related Conditionals p  q If a polygon has 6 sides, then it is a hexagon. Converse: q  p , hypothesis & conclusion switch If a polygon is a hexagon, then it has 6 sides. Inverse: ~p  ~q , negate both hypothesis and conclusion If a polygon does not have 6 sides, then it is not hexagon. Contrapositive: ~q  ~p , negate both hypothesis and conclusion of the converse If a polygon is not a hexagon, then it does not have 6 sides. Related Conditionals

Converse (q  p) & Inverse (~p  ~q) are either LESSON 2-3: Conditional Statements Logically Equivalent Conditional (p  q) & Contrapositive (~q  ~p) are either both TRUE or both FALSE Converse (q  p) & Inverse (~p  ~q) are either both TRUE or both FALSE Logically Equivalent

All squares are quadrilaterals. LESSON 2-3: Conditional Statements EXAMPLE 3 Related Conditionals 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. All squares are quadrilaterals. Conditional: Converse: Inverse: Contrapositive: Example 4

All whole numbers are integers. LESSON 2-3: Conditional Statements EXAMPLE 3 Related Conditionals 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. All whole numbers are integers. Conditional: Converse: Inverse: Contrapositive: Example 4