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* Given an equation, you can … * Add the same value (or equivalent values) to both sides, If a = b, then a + 7 = b + 7 * Subtract the same value (or equivalent values) from both sides, If a = b, then a - 7 = b - 7 * Multiply both sides by the same value (or equivalent values), If a = b, then 7a = 7b * Divide both sides by the same value (or equivalent values), If a = b, then a/7 = b/7 Reflexive Property: a = a (A value is equal to itself.) Reflexive Property Examples:: AB AB or 1 1 or 15 15 Symmetric Property: If a = b, then b = a. (Reverse order) Symmetric Property Examples: if AB CD then CD AB or if 1 2 then 2 1 * Substitution Property: if a = b & a = c, then c = b. 1st equation: (a = b): is given to be true; 2nd equation (a = c): indicates a & c are equivalent 3rd equation (c = b): rewrite of 1st equation with c substituted for a Example: (Substitution method for simultaneous equations) x+y=5 (Given) y = 13 (Establishes that y & 13 are equivalent) x + 13 = 5 (Substitute 13 for y in 1st equation) * Transitive Property : if a = b & b = c, then a = c. a=c Note: You can distinguish between Substitution Property and Transitive Property by the order of the values in the 2 equations. In proofs you are allowed to use them interchangeably. Substitution Property: if AB CD & AB EF then EF CD or if 1 2 & 1 3 then 3 2 Transitive Property: if AB CD & CD EF then AB EF or if 1 2 & 2 3 then 1 3 Prove: If 3x = 7 - .5x then x = 2. Given: 3x = 7 - .5x Prove: x = 2 Proof: Reasons Statements 1. 3x = 7 - .5x 1. Given 2. 6x = 14 - x 2. Multiplication Property of Equality 3. 7x = 14 3. Addition Property of Equality 4. x=2 4. Division Property of Equality Given: m1 m3 Prove: DEG HEF Proof: Statements 1. m1 m3 H G 1 D 2 3 E F Reasons 1. Given 2. m1 m2 m2 m3 2. Add. Property of = 3. m1 m2 mDEG 3. Angle Add. Post. 4. m2 m3 mHEF 5. mDEG mHEF 4. Angle Add. Post 5. Substitution (3 & 4 into 2) 6. DEG HEF 6. Def. of congruent angles