Geometry 2-2 Complete Lesson: Conditional Statements

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Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you cannot read this, then you are not too close." Explain.

1

Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you are not too close, then you cannot read this." Explain.

10

Problem 1 Got It?

10

Problem 2 Got It?

10

Take Note: Define truth value.

10

Take Note: Describe how a counterexample can help you identify the truth value of a conditional.

10

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

10

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

10

Take Note: Define negation.

5

Take Note: Type the symbol used to represent negation.

Enter only one character.

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Take Note: Categorize the items on the left based on which type of conditional they represent.

\sim p \rightarrow \sim q
q \rightarrow p
If not q, then not p.
Exchange the hypothesis and conclusion of the original conditional.
p \rightarrow q

Conditional
Converse
Inverse
Contrapositive

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Problem 4 Got It? What is the converse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

What is the truth value of the converse? If the converse is false, give a counterexample.

10

Problem 4 Got It? What is the inverse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

10

Problem 4 Got It? What is the contrapositive of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

30

Vocabulary: What are the hypothesis and the conclusion of the following statement? Write it as a conditional in if-then form.

Residents of Key West live in Florida.

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Vocabulary: What are the converse, inverse, and contrapositive of the statement? Which statements are true?

If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm.

10

Error Analysis: Your classmate rewrote the statement "You jog every Sunday." as the following conditional. What is your classmate's error? Correct it.

If you jog, then it is Sunday.

10

Reasoning: Suppose a conditional statement and its converse are both true. What are the truth values of the contrapositive and inverse? How do you know?

10

Review Lesson 2-1: Sketch a counterexample on the canvas to show that the statement is false.

You can connect any four points to form a rectangle.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

10

Review Lesson 1-8: Find the perimeter of a rectangle with the given base and height.

6 in., 12 in.

Enter the perimeter using the same format shown in the problem: "6 in."

5

Vocabulary Review: Identify the conclusion of the statement.

If the weather is nice, we will go swimming.

10

Geometry 2-2 Complete Lesson: Conditional Statements

Solve It! Suppose the statement is true, "If you are too close, then you can read this." Is this statement also true? "If you cannot read this, then you are not too close." Explain.

Solve It! Suppose the statement is true, "If you are too close, then you can read this." Is this statement also true? "If you are not too close, then you cannot read this." Explain.

Problem 1 Got It?

Problem 2 Got It?

Take Note: Define truth value.

Take Note: Describe how a counterexample can help you identify the truth value of a conditional.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas. If a month has 28 days, then it is February.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.If two angles form a linear pair, then they are supplementary.

Take Note: Define negation.

Take Note: Type the symbol used to represent negation.Enter only one character.

Take Note: Categorize the items on the left based on which type of conditional they represent.

Problem 4 Got It? What is the converse of the conditional statement? If a vegetable is a carrot, then it contains beta carotene. What is the truth value of the converse? If the converse is false, give a counterexample.

Problem 4 Got It? What is the inverse of the conditional statement? If a vegetable is a carrot, then it contains beta carotene.

Problem 4 Got It? What is the contrapositive of the conditional statement? If a vegetable is a carrot, then it contains beta carotene.

Vocabulary: What are the hypothesis and the conclusion of the following statement? Write it as a conditional in if-then form.Residents of Key West live in Florida.

Vocabulary: What are the converse, inverse, and contrapositive of the statement? Which statements are true?If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm.

Error Analysis: Your classmate rewrote the statement "You jog every Sunday." as the following conditional. What is your classmate's error? Correct it.If you jog, then it is Sunday.

Reasoning: Suppose a conditional statement and its converse are both true. What are the truth values of the contrapositive and inverse? How do you know?

Review Lesson 2-1: Sketch a counterexample on the canvas to show that the statement is false.You can connect any four points to form a rectangle.You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Review Lesson 1-8: Find the perimeter of a rectangle with the given base and height.6 in., 12 in.Enter the perimeter using the same format shown in the problem: "6 in."

Vocabulary Review: Identify the conclusion of the statement.If the weather is nice, we will go swimming.

Reflection: Math Success

Solve It! Suppose the statement is true, "If you are too close, then you can read this." Is this statement also true? "If you cannot read this, then you are not too close." Explain.

Solve It! Suppose the statement is true, "If you are too close, then you can read this." Is this statement also true? "If you are not too close, then you cannot read this." Explain.

Problem 1 Got It?

Problem 2 Got It?

Take Note: Define truth value.

Take Note: Describe how a counterexample can help you identify the truth value of a conditional.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas. If a month has 28 days, then it is February.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.If two angles form a linear pair, then they are supplementary.

Take Note: Define negation.

Take Note: Type the symbol used to represent negation.Enter only one character.

Take Note: Which statement always has an equivalent truth value with the conditional?

Take Note: Which statement always has an equivalent truth value with the inverse?

Take Note: Categorize the items on the left based on which type of conditional they represent.

Problem 4 Got It? What is the converse of the conditional statement? If a vegetable is a carrot, then it contains beta carotene. What is the truth value of the converse? If the converse is false, give a counterexample.

Problem 4 Got It? What is the inverse of the conditional statement? If a vegetable is a carrot, then it contains beta carotene.

Problem 4 Got It? What is the contrapositive of the conditional statement? If a vegetable is a carrot, then it contains beta carotene.

Vocabulary: What are the hypothesis and the conclusion of the following statement? Write it as a conditional in if-then form.Residents of Key West live in Florida.

Vocabulary: What are the converse, inverse, and contrapositive of the statement? Which statements are true?If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm.

Error Analysis: Your classmate rewrote the statement "You jog every Sunday." as the following conditional. What is your classmate's error? Correct it.If you jog, then it is Sunday.

Reasoning: Suppose a conditional statement and its converse are both true. What are the truth values of the contrapositive and inverse? How do you know?

Review Lesson 2-1: Sketch a counterexample on the canvas to show that the statement is false.You can connect any four points to form a rectangle.You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Review Lesson 1-8: Find the perimeter of a rectangle with the given base and height.6 in., 12 in.Enter the perimeter using the same format shown in the problem: "6 in."

Vocabulary Review: Identify the conclusion of the statement.If the weather is nice, we will go swimming.

Reflection: Math Success

Take Note: Which statement always has an equivalent truth value with the conditional?

Take Note: Which statement always has an equivalent truth value with the inverse?

Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you cannot read this, then you are not too close." Explain.

Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you are not too close, then you cannot read this." Explain.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

Take Note: Type the symbol used to represent negation.

Enter only one character.

Problem 4 Got It? What is the converse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

What is the truth value of the converse? If the converse is false, give a counterexample.

Problem 4 Got It? What is the inverse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

Problem 4 Got It? What is the contrapositive of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

Vocabulary: What are the hypothesis and the conclusion of the following statement? Write it as a conditional in if-then form.

Residents of Key West live in Florida.

Vocabulary: What are the converse, inverse, and contrapositive of the statement? Which statements are true?

If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm.

Error Analysis: Your classmate rewrote the statement "You jog every Sunday." as the following conditional. What is your classmate's error? Correct it.

If you jog, then it is Sunday.

Review Lesson 2-1: Sketch a counterexample on the canvas to show that the statement is false.

You can connect any four points to form a rectangle.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Review Lesson 1-8: Find the perimeter of a rectangle with the given base and height.

6 in., 12 in.

Enter the perimeter using the same format shown in the problem: "6 in."

Vocabulary Review: Identify the conclusion of the statement.

If the weather is nice, we will go swimming.

Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you cannot read this, then you are not too close." Explain.

Solve It! Suppose the statement is true, "If you are too close, then you can read this."
Is this statement also true? "If you are not too close, then you cannot read this." Explain.

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

Problem 3 Got It? Is the conditional true or false? If it is false, provide a counterexample on the canvas.

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

Take Note: Type the symbol used to represent negation.

Enter only one character.

Problem 4 Got It? What is the converse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

What is the truth value of the converse? If the converse is false, give a counterexample.

Problem 4 Got It? What is the inverse of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

Problem 4 Got It? What is the contrapositive of the conditional statement?

If a vegetable is a carrot, then it contains beta carotene.

Vocabulary: What are the hypothesis and the conclusion of the following statement? Write it as a conditional in if-then form.

Residents of Key West live in Florida.

Vocabulary: What are the converse, inverse, and contrapositive of the statement? Which statements are true?

If a figure is a rectangle with sides 2 cm and 3 cm, then it has a perimeter of 10 cm.

Error Analysis: Your classmate rewrote the statement "You jog every Sunday." as the following conditional. What is your classmate's error? Correct it.

If you jog, then it is Sunday.

Review Lesson 2-1: Sketch a counterexample on the canvas to show that the statement is false.

You can connect any four points to form a rectangle.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Review Lesson 1-8: Find the perimeter of a rectangle with the given base and height.

6 in., 12 in.

Enter the perimeter using the same format shown in the problem: "6 in."

Vocabulary Review: Identify the conclusion of the statement.

If the weather is nice, we will go swimming.