2.4 Vocabulary equation “solve” an equation formula mathematical reasoning Mathematical reasoning uses algebraic properties to justify steps when solving an equation

The Distributive Property: a(b + c) = ab + ac The Commutative Property: a + b = b + c

Example 1: Solving an Equation in Algebra Solve the equation 4m – 8 = –12. Write a justification for each step. 4m – 8 = –12 4m = –4 m = –1

Example 2 Solve the equation . Write a justification for each step. t = –14

Example 3: Problem-Solving Application What is the temperature in degrees Fahrenheit F when it is 15°C? Solve the equation F = C + 32 for F and justify each step. 9 5

Like algebra, geometry also uses numbers, variables, and operations Like algebra, geometry also uses numbers, variables, and operations. For example, segment lengths and angle measures are numbers. So you can use these same properties of equality to write algebraic proofs in geometry. A B AB represents the length AB, so you can think of AB as a variable representing a number. Likewise, mA a variable representing the magnitude of A. Helpful Hint

Example 4: Solving an Equation in Geometry Write a justification for each step. NO = NM + MO 4x – 4 = 2x + (3x – 9) 4x – 4 = 5x – 9 –4 = x – 9 5 = x

Example 5 Write a justification for each step. mABC = mABD + mDBC 8x° = (3x + 5)° + (6x – 16)° 8x = 9x – 11 –x = –11 x = 11

EXAMPLE 5: Show the perimeter of triangle ABC is equal to the perimeter triangle CDA and justify each step. A B D C 1. AB  CD 2. BC  DA 3. AB = CD 4. BC = DA 5. CA = AC 6. PΔABC = AB +BC +CA 7. PΔCDA = CD +DA +AC 8. PΔABC = CD +DA +AC 9. PΔABC = PΔCDA