Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
2-4 Reasoning in Algebra Objectives: • Use basic properties of algebra in reasoning • Define congruence • State the properties of congruence 1 Properties of Equality Addition Property If a = b, then a + c = b + c Subtraction Property If a = b, then a – c = b – c Multiplication Property If a = b, then a * c = b * c Division Property If a = b and c ≠ 0, then a/c = b/c Reflexive Property a=a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c Substitution Property If a = b, then b can replace a in any expression Distributive Property a(b + c) = ab + ac 2 Solve and Write a Justification for Each Step 2 (x + 1) = 8 Given 2x + 2 = 8 Distributive Property 2x =6 Subtraction Property of = x =3 Division Property of = 3 Congruence in Geometry • Congruence – Having the same shape and size • Symbol for congruence ≅ • AB ≅ CD (Segment AB is congruent to segment CD.) A B C D •∠ A ≅ ∠ B (Angle A is congruent to angle B.) A B 4 Properties of Congruence • Reflexive Property AB ≅ AB ∠A≅∠A • Symmetric Property If AB ≅ CD, then CD ≅ AB If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A • Transitive Property If AB ≅ CD and CD ≅ EF, then AB ≅ EF If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C,then ∠ A ≅ ∠ C 5