Chapter 2: Geometric Reasoning Section 2.4: Biconditional Statements and Definitions

Transcription

1 Name: Date: Chapter 2: Geometric Reasoning Section 2.4: Biconditional Statements and Definitions Geometry B Are you ready? Write a conditional statement for problems 1 and The intersection of two lines is a point. 2. An odd number is one more than a multiple of Write the converse of the conditional If Pedro lives in Chicago, then he lives in Illinois. Find its truth value. Objectives of Lesson: A biconditional statement Writing Math: Example 1: Identifying the Conditionals within a Biconditional Statement Write the conditional statement and converse within the biconditional. An angle is obtuse if and only if its measure is greater than 90 and less than 180.

2 Example 2: Identifying the Conditionals within a Biconditional Statement Write the conditional statement and converse within the biconditional. A solution is neutral its ph is 7. 2 Example 3: Write the conditional statement and converse within the biconditional. An angle is acute iff its measure is greater than 0 and less than 90. Example 4: Write the conditional statement and converse within the biconditional. Cho is a member if and only if he has paid the $5 dues. Example 5: Identifying the Conditionals within a Biconditional Statement For each conditional, write the converse and a biconditional statement. A. If 5x 8 = 37, then x = 9.

3 B. If two angles have the same measure, then they are congruent. 3 Example 6: For each conditional, write the converse and a biconditional statement. If the date is July 4th, then it is Independence Day. Example 7: For each conditional, write the converse and a biconditional statement. If points lie on the same line, then they are collinear. Example 8: Analyzing the Truth Value of a Biconditional Statement Determine if the biconditional is true. If false, give a counterexample. A rectangle has side lengths of 12 cm and 25 cm if and only if its area is 300 cm 2.

4 4 Example 9: Analyzing the Truth Value of a Biconditional Statement Determine if the biconditional is true. If false, give a counterexample. A natural number n is odd n 2 is odd. Example 10: Analyzing the Truth Value of a Biconditional Statement Determine if the biconditional is true. If false, give a counterexample. An angle is a right angle iff its measure is 90. Example 10: Determine if the biconditional is true. If false, give a counterexample. y = 5 y 2 = 25 A definition In the glossary, a polygon is defined as a closed plane figure formed by three or more line segments. A triangle is defined as a three-sided polygon, and a quadrilateral is a foursided polygon. Helpful Hint Example 12: Writing Definitions as Biconditional Statements Write each definition as a biconditional. A. A pentagon is a five-sided polygon.

5 B. A right angle measures Example 13: Write each definition as a biconditional. a. A quadrilateral is a four-sided polygon. b. The measure of a straight angle is For the conditional If an angle is right, then its measure is 90, write the converse and a biconditional statement. 2. Determine if the biconditional Two angles are complementary if and only if they are both acute is true. If false, give a counterexample. 3. Write the definition An acute triangle is a triangle with three acute angles as a biconditional.

6 Write the conditional statement and converse within each biconditional. 4) Perry can paint the entire living room if and only if he has enough paint. 6 5) Your medicine will be ready by 5 P.M. if and only if you drop your prescription off by 8 A.M. For each conditional, write the converse and a biconditional statement. 6) If a student is a sophomore, then the student is in the tenth grade. 7) If two segments have the same length, then they are congruent. smilardo.wordpress.com - homework: worksheets: link to book and