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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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.

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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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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.

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

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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.

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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?

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.

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.