Geometry 2-3 Complete Lesson: Biconditionals and Definitions

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Solve It! Look at the examples of the insects and noninsects below.
How would you complete the following sentence: "If an animal is an insect then..."? Explain your reasoning.

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Take Note: Define biconditional.

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Take Note: How can you determine if a conditional statement can be written as a biconditional?

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Take Note: Provide an example of a biconditional statement.

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Problem 1 Got It? What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional.
If two angles have equal measure, then the angles are congruent.

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Problem 2 Got It? What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1.

A

B

C

D

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Take Note: What are the three important components of a good definition?

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Problem 3 Got It? Is the definition of straight angle reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180°.

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Take Note: Describe how a counterexample can be used to identify poor definitions.

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Problem 4 Got It? Is the following statement a good definition? Explain.
A square is a figure with four right angles.

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Problem 4 Got It? Reasoning: How can you rewrite the statement so that it is a good definition?
Obtuse angles have greater measures than acute angles.

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A

B

C

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A

B

C

D

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A

B

C

D

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Vocabulary: Explain how the term biconditional is fitting for a statement composed of two conditionals.

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Error Analysis: Why is the following statement a poor definition?
Elephants are gigantic animals.

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Compare and Contrast: Which of the following statements is a better definition of a linear pair? Explain.
A linear pair is a pair of supplementary angles.
A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

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Review Lesson 2-2: Identify the converse of the statement.
If you do not sleep enough, then your grades suffer.

If your grades suffer, then you did not sleep enough.

If your grades do not suffer, then you slept enough.

If you sleep enough, then your grades do not suffer.

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Review Lesson 2-2: What is the truth value of a the contrapositive of a true conditional?

Tačno

Netačno

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Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

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Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

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Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

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Vocabulary Review: Identify the hypothesis of the statement.
If it rains on Friday, I won't have to cut the grass on Saturday.

it rains on Friday

I won't have to cut the grass on Sunday

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Use Your Vocabulary: Match each word on the left with its meaning on the right.

Stavka koja se može prevući		Odgovarajuća stavka
bipartisan (adjective)		occurring every two years
bicoastal (adjective)		a two-event athletic contest
biplane (noun)		occurring every two hundred years
bicentennial (adjective)		having two coasts
biathlon (noun)		supported by two parties
biweekly (adjective)		a two-footed animal
biped (noun)		a plane with two sets of wings
biannually (adverb)		occurring every two weeks

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Geometry 2-3 Complete Lesson: Biconditionals and Definitions

Solve It! Look at the examples of the insects and noninsects below. How would you complete the following sentence: "If an animal is an insect then..."? Explain your reasoning.

Take Note: Define biconditional.

Take Note: How can you determine if a conditional statement can be written as a biconditional?

Take Note: Provide an example of a biconditional statement.

Problem 1 Got It? What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional. If two angles have equal measure, then the angles are congruent.

Problem 2 Got It? What are the two conditionals that form this biconditional? Two numbers are reciprocals if and only if their product is 1.

Take Note: What are the three important components of a good definition?

Problem 3 Got It? Is the definition of straight angle reversible? If yes, write it as a true biconditional.A straight angle is an angle that measures 180°.

Take Note: Describe how a counterexample can be used to identify poor definitions.

Problem 4 Got It? Is the following statement a good definition? Explain.A square is a figure with four right angles.

Problem 4 Got It? Reasoning: How can you rewrite the statement so that it is a good definition? Obtuse angles have greater measures than acute angles.

Vocabulary: Explain how the term biconditional is fitting for a statement composed of two conditionals.

Error Analysis: Why is the following statement a poor definition?Elephants are gigantic animals.

Compare and Contrast: Which of the following statements is a better definition of a linear pair? Explain.A linear pair is a pair of supplementary angles.A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

Review Lesson 2-2: Identify the converse of the statement.If you do not sleep enough, then your grades suffer.

Review Lesson 2-2: What is the truth value of a the contrapositive of a true conditional?

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Vocabulary Review: Identify the hypothesis of the statement.If it rains on Friday, I won't have to cut the grass on Saturday.

Use Your Vocabulary: Match each word on the left with its meaning on the right.

Reflection: Math Success

Solve It! Look at the examples of the insects and noninsects below. How would you complete the following sentence: "If an animal is an insect then..."? Explain your reasoning.

Take Note: Define biconditional.

Take Note: How can you determine if a conditional statement can be written as a biconditional?

Take Note: Provide an example of a biconditional statement.

Problem 1 Got It? What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional. If two angles have equal measure, then the angles are congruent.

Problem 2 Got It? What are the two conditionals that form this biconditional? Two numbers are reciprocals if and only if their product is 1.

Take Note: What are the three important components of a good definition?

Problem 3 Got It? Is the definition of straight angle reversible? If yes, write it as a true biconditional.A straight angle is an angle that measures 180°.

Take Note: Describe how a counterexample can be used to identify poor definitions.

Problem 4 Got It? Is the following statement a good definition? Explain.A square is a figure with four right angles.

Problem 4 Got It? Reasoning: How can you rewrite the statement so that it is a good definition? Obtuse angles have greater measures than acute angles.

Vocabulary: Explain how the term biconditional is fitting for a statement composed of two conditionals.

Error Analysis: Why is the following statement a poor definition?Elephants are gigantic animals.

Compare and Contrast: Which of the following statements is a better definition of a linear pair? Explain.A linear pair is a pair of supplementary angles.A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

Review Lesson 2-2: Identify the converse of the statement.If you do not sleep enough, then your grades suffer.

Review Lesson 2-2: What is the truth value of a the contrapositive of a true conditional?

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Review Lesson 2-1: What is the next term in the sequence? Enter only a number.

Vocabulary Review: Identify the hypothesis of the statement.If it rains on Friday, I won't have to cut the grass on Saturday.

Use Your Vocabulary: Match each word on the left with its meaning on the right.

Reflection: Math Success

Solve It! Look at the examples of the insects and noninsects below.
How would you complete the following sentence: "If an animal is an insect then..."? Explain your reasoning.

Problem 1 Got It? What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional.
If two angles have equal measure, then the angles are congruent.

Problem 2 Got It? What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1.

Problem 3 Got It? Is the definition of straight angle reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180°.

Problem 4 Got It? Is the following statement a good definition? Explain.
A square is a figure with four right angles.

Problem 4 Got It? Reasoning: How can you rewrite the statement so that it is a good definition?
Obtuse angles have greater measures than acute angles.

Error Analysis: Why is the following statement a poor definition?
Elephants are gigantic animals.

Compare and Contrast: Which of the following statements is a better definition of a linear pair? Explain.
A linear pair is a pair of supplementary angles.
A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

Review Lesson 2-2: Identify the converse of the statement.
If you do not sleep enough, then your grades suffer.

Vocabulary Review: Identify the hypothesis of the statement.
If it rains on Friday, I won't have to cut the grass on Saturday.

Solve It! Look at the examples of the insects and noninsects below.
How would you complete the following sentence: "If an animal is an insect then..."? Explain your reasoning.

Problem 1 Got It? What is the converse of the following true conditional? If the converse is also true, rewrite the statements as a biconditional.
If two angles have equal measure, then the angles are congruent.

Problem 2 Got It? What are the two conditionals that form this biconditional?
Two numbers are reciprocals if and only if their product is 1.

Problem 3 Got It? Is the definition of straight angle reversible? If yes, write it as a true biconditional.
A straight angle is an angle that measures 180°.

Problem 4 Got It? Is the following statement a good definition? Explain.
A square is a figure with four right angles.

Problem 4 Got It? Reasoning: How can you rewrite the statement so that it is a good definition?
Obtuse angles have greater measures than acute angles.

Error Analysis: Why is the following statement a poor definition?
Elephants are gigantic animals.

Compare and Contrast: Which of the following statements is a better definition of a linear pair? Explain.
A linear pair is a pair of supplementary angles.
A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

Review Lesson 2-2: Identify the converse of the statement.
If you do not sleep enough, then your grades suffer.

Vocabulary Review: Identify the hypothesis of the statement.
If it rains on Friday, I won't have to cut the grass on Saturday.