1. 2.4 Vocabulary equation “solve” an equation mathematical reasoning
Mathematical reasoning uses algebraic properties to justify steps when solving an equation

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

3. 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

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

5. 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

6. 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

7. 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

8. 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

9. 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