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Chapter 2 Section 2.2 Definitions and Biconditionals Perpendicular • Two lines are perpendicular if they intersect to form a right angle. • A line is perpendicular to a plane if it intersects the plane and is perpendicular to every line in the plane. l m lm Use the diagram to determine if the statement is true or false True True True False False True False Biconditional • A statement that contains the words “if and only if” • A biconditional is equivalent to writing a conditional statement and its converse – Example: Three lines are coplanar if and only if they lie in the same plane. • Conditional: If three lines are coplanar then they lie in the same plane. • Converse: If three lines lie in the same plane then they are coplanar – The biconditional means both the conditional and its converse are true Rewrite each biconditional statement as a conditional and its converse 8. x = 4 if and only if x2 = 16 1. If x = 4 then x2 = 16 2. If x2 = 16 then x = 4 9. Point Y lies between X and Z if and only if XY + YZ = XZ 1. If point Y lies between X and Z then XY + YZ = XZ 2. If XY + YZ = XZ then point Y lies between X and Z 10. The car will run if and only if there is gas in the tank 1. If the car will run then there is gas in the tank 2. If there is gas in the tank then the car will run Rewrite each biconditional statement as a conditional and its converse 11. Two angles are congruent if and only if they have the same measure 1. If two angles are congruent then they have the same measure 2. If two angles have the same measure then they are congruent 12. An angle is a right angle if and only if it measures 90 1. If an angle is a right angle then it measures 90 2. If an angle measures 90 then it is a right angle Write the converse of each true statement. If it is true combine them to write a true biconditional 13. If you are 15 years old then you are a teenager 1. If you are a teenager, then you are 15 years old 2. FALSE 14. If point C is on Ray BA, then point C is on line BA 1. If point C is on line BA then point C is on Ray BA 2. False Write the converse of each true statement. If it is true combine them to write a true biconditional 15. If two angles are complementary then the sum of their measures is 90 1. If two angles have a sum of 90 then they are complementary (TRUE) 2. Two angles are complementary if and only if their sum is 90. 16. If point C is between A and B, then Ray CA and Ray CB are opposite rays 1. If ray CA and Ray CB are opposite rays then point C is between A and B (TRUE) 2. Point C is between A and B if and only if ray CA and ray CB are opposite rays Write the converse of each true statement. If it is true combine them to write a true biconditional 17. If two angles form a linear pair then they are adjacent 1. If two angles are adjacent then they forma linear pair 2. False 18. Write a definition of an E-flat baritone saxophone 1. A saxophone that has a frequency of 69 cycles per second to 416 cycles per second is called an E-Flat baritone sax 19. Tell whether the following conditional is true, if not explain why. 1. If a note played on a saxophone has a frequency of 610 cycles per second then the saxophone is an E-flat alto saxophone 2. False: It could be a B-flat tenor saxophone HW #16 Pg 82-83 13-31