EXPLAIN 1 Introducing Proofs Read Explain 1 and complete Your Turn 1 3 adapted from Lesson 1 4 A conjecture is a statement that is believed to be true You can use inductive or deductive reasoning to show or prove that a conjecture is true Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true Deductive reasoning is the process of using logic to draw conclusions A conditional statement is a statement that can be written in the form If p then q where p is the hypothesis and q is the conclusion For example in the conditional statement If 3x 5 13 then x 6 the hypothesis is 3x5 13 and the conclusion is x 6 Most of the Properties of Equality can be written as conditional statements You can use these properties to solve an equation like 3x 5 13 to prove that x 6 Properties of Equality Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution Property of Equality Example Use deductive reasoning to solve the equation Use properties of Equality to justify each step 1 14 3x 4 18 3x If ab then a c b c If ab then a c b c If ab then ac bc If a b and c 0 then ama If a b then b a If a band b c then a c If ab then b can be substituted for a in any expression 6 x x 6 Addition Property of Equality Division Property of Equality Symmetric Property of Equality Your Turn 1 Identify the Property of Equality that is used in each statement If x 2 then 2x 4 5 3a therefore 3a 5 If T 4 then 5T 7 equals 27 If 9 4x and 4x m then 9 m