Geometry 2-3 Complete Lesson: Biconditionals and Definitions

Last updated about 4 years ago

25 questions

Geometry 2-3 Complete Lesson: Biconditionals and Definitions

Last updated about 4 years ago

25 questions

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.

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.

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

Geometry 2-3 Complete Lesson: Biconditionals and Definitions

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.

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.

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 2-1: 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.

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.

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

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

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 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.

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 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.

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.