Geometry 2-3 Complete Lesson: Biconditionals and Definitions
By Matthew Richardson
star
star
star
star
star
Last updated over 3 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.
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: Define biconditional.
Take Note: How can you determine if a conditional statement can be written as a 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.
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 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 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?
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°.
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.
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? 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.
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.
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.
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.
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: 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 2-2: 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.
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.
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.
Use Your Vocabulary: Match each word on the left with its meaning on the right.
| Draggable item | arrow_right_alt | Category |
|---|---|---|
biathlon (noun) | arrow_right_alt | occurring every two years |
bicentennial (adjective) | arrow_right_alt | a two-event athletic contest |
biannually (adverb) | arrow_right_alt | occurring every two hundred years |
biped (noun) | arrow_right_alt | having two coasts |
bicoastal (adjective) | arrow_right_alt | supported by two parties |
biplane (noun) | arrow_right_alt | a two-footed animal |
biweekly (adjective) | arrow_right_alt | a plane with two sets of wings |
bipartisan (adjective) | arrow_right_alt | occurring every two weeks |
Reflection: Math Success
Reflection: Math Success