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.

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Presentation transcript:

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.) Symmetric Property: If a = b, then b = a. (Reverse order) Reflexive Property Examples:: Symmetric Property Examples: or

Substitution Property: if a = b & a = c, then c = b. x + y = 5 (Given) 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 y = 13 (Establishes that y & 13 are equivalent) x + 13 = 5 (Substitute 13 for y in 1st equation) Example: (Substitution method for simultaneous equations)

Transitive Property : if a = b & b = c, then a = c. a = ca = 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: or Transitive Property:

Prove: If 3x = 7 -.5x then x = 2. Given: 3x = 7 -.5x Prove: x = 2 Proof: Statements Reasons 1. 3x = 7 -.5x 1. Given 2. 6x = 14 - x2. Multiplication Property of Equality 3. 7x = 143. Addition Property of Equality 4. x = 2 4. Division Property of Equality

Proof: Statements Reasons 2. Add. Property of = 3. Angle Add. Post. 4. Angle Add. Post Given Substitution (3 & 4 into 2) Def. of congruent angles Given: Prove: 13 2 G F H ED