AMSCO'S Geometry. New York - Rye High School

116 Proving Statements in GeometryFrom y x 7 and x 3, we can conclude that y 3 7. This is not anexample of the transitive property of equality. We have used the substitutionproperty to replace x with its equal, 3, in the equation y x 7.We use this postulate frequently in algebra. For example, if we find the solutionof an equation, we can substitute that solution to show that we have a truestatement.4x 1 3x 7Checkx 8 4x 1 3x 74(8) 1 3(8) 731 31 ✔In a system of two equations in two variables, x and y, we can solve oneequation for y and substitute in the other equation. For example, we are usingthe substitution postulate in the third line of this solution:5 ?3x 2y 13y x 13x 2(x 1) 133x 2x 2 135x 15x 3y 3 1 2EXAMPLE 1Given: CE 2CD and CD DEProve: CE 2DEProof Statements Reasons1. CE 2CD 1. Given.2. CD DE 2. Given.3. CE 2DE 3. Substitution postulate. (Or: Aquantity may be substituted forits equal in any expression ofequality.)